1001 Solved Problems In Engineering Mathematics By Excel Academic Council Better ((top))
1001 Solved Problems in Engineering Mathematics , published by the Excel Academic Council, is widely considered a staple resource for engineering students, particularly those preparing for licensure board exams. Often associated with authors Jaime R. Tiong and Romeo A. Rojas Jr., the book is prized for its structured, practical approach to mastering complex mathematical concepts. Core Structure and Content
The book is meticulously organized to serve as a comprehensive study plan, often divided into a 23-day curriculum. Each section typically includes:
Summarized Formulas and Concepts: Brief theory sections and "Tips & Trivia" to refresh fundamental knowledge before diving into practice.
Multiple-Choice Problems: Designed to mimic the format of actual board exams, such as the Electronics Engineering (ECE) board exam.
Detailed Solutions: Complete, step-by-step solutions for every problem, allowing students to bridge the gap between theory and application. Subjects Covered
The collection spans a broad range of engineering mathematics, progressing from foundational to advanced topics:
Fundamentals: Systems of numbers, conversions, and basic algebra.
Intermediate Math: Trigonometry, logarithms, and coordinate geometry.
Advanced Topics: Differential and integral calculus, differential equations, and matrix algebra.
Specialized Areas: Probability, statistics, and engineering science subjects. Why It Is Highly Regarded
Students and educators recommend this resource because it focuses on active problem-solving rather than passive reading. By providing 1001 unique problems, it ensures that learners encounter a wide variety of scenarios they might face in professional examinations or real-world engineering tasks.
Resources for this book, including video walkthroughs and PDF previews, can be found on platforms like TikTok, YouTube, and Scribd. Are you preparing for a specific board exam, or
Case Study: Passing the Board Exam with 1001 Problems
Consider the story of thousands of topnotchers across the Philippines. When interviewed, the common answer to "What reviewer did you use for Math?" is often: "1001 Solved Problems in Engineering Mathematics by Excel."
Why? Because the board exam rarely invents new math. It recycles concepts. The Excel Academic Council has curated 1,001 problems that represent nearly every "type" of problem that has appeared on the PRC board exams in the last 20 years.
For example:
- Differential Calculus: If you master the 40 time-rate problems in this book (flowing water, revolving lights, ladder sliding), you will encounter no surprises on exam day.
- Integral Calculus: The 30 problems on "volume by revolution" cover circular rings, washers, and cylindrical shells—every possible axis of rotation.
If you can solve 850 out of the 1,001 problems without looking at the solution key, you are mathematically ready to pass. It’s that simple.
✅ Step 2 – Active recall, not passive reading
Don’t just read the solved problem and nod along.
Do this instead:
- Cover the solution with a sticky note or card.
- Attempt the problem on paper – show all steps.
- Uncover the solution only after finishing or getting stuck.
- Mark your result:
- ✓ = correct on first try
- ~ = correct but slow/messy
- ✗ = wrong or couldn’t finish
Feature: 1001 Solved Problems in Engineering Mathematics — Excel Academic Council
Overview
- Title: 1001 Solved Problems in Engineering Mathematics
- Author/Editor: Excel Academic Council
- Type: Problem-solution compendium / reference workbook
- Audience: Undergraduate and postgraduate engineering students, instructors, and practicing engineers seeking worked examples and problem-solving techniques.
Key Selling Points
- Comprehensive coverage across core engineering mathematics topics.
- Large problem set (1,001) with fully worked solutions emphasizing methods and applications.
- Step-by-step solution style aimed at learning problem-solving, not just final answers.
- Practical focus: engineering examples, modelling tips, and numerical solution techniques.
- Useful as a course supplement, self-study guide, and exam prep resource.
Contents (structured by major topics)
- Calculus
- Limits and continuity
- Differential calculus: derivatives, implicit differentiation, maxima/minima
- Integral calculus: definite/indefinite integrals, techniques, improper integrals
- Applications: area, volume, centre of mass
- Multiple integrals and change of variables
- Ordinary Differential Equations (ODEs)
- First-order ODEs: separable, linear, exact, integrating factors
- Higher-order linear ODEs with constant coefficients
- Method of undetermined coefficients, variation of parameters
- Systems of ODEs and eigenvalue methods
- Laplace transforms and ODE applications
- Linear Algebra
- Matrices and determinants
- Systems of linear equations: Gaussian elimination
- Vector spaces, linear independence, basis, dimension
- Eigenvalues, eigenvectors, diagonalization
- Applications to circuits, structures, and stability analysis
- Complex Analysis
- Complex numbers, polar form
- Analytic functions, Cauchy-Riemann equations
- Complex integration, Cauchy’s theorem, residues and contour integration
- Vector Calculus
- Gradient, divergence, curl
- Line, surface, and volume integrals
- Green’s, Stokes’, and Divergence theorems with worked engineering examples
- Probability & Statistics
- Probability distributions, expectation, variance
- Common distributions (Binomial, Poisson, Normal)
- Statistical estimation, hypothesis testing, regression basics
- Reliability and life-data analysis examples
- Numerical Methods
- Root-finding: bisection, Newton-Raphson, secant
- Interpolation and polynomial approximation
- Numerical integration and differentiation
- Numerical solution of ODEs: Euler, Runge-Kutta methods
- Error analysis and stability considerations
- Transform Methods & Fourier Series
- Fourier series, convergence, Gibbs phenomenon
- Fourier transforms, discrete Fourier transform basics
- Laplace transforms for engineering applications
- Optimization & Calculus of Variations
- Unconstrained and constrained optimization (Lagrange multipliers, KKT)
- Simple variational problems and Euler-Lagrange equations
- Special Functions & Miscellany
- Gamma, Beta functions, Bessel functions basics
- Orthogonal functions and applications to PDEs
Structure and Pedagogy
- Each chapter begins with a brief theoretical summary and key formulas.
- Problems organized by difficulty: Basic (foundation), Intermediate (application), Advanced (complex/multi-step).
- For each problem:
- Clear problem statement.
- Strategy/approach outline.
- Step-by-step solution with intermediate steps shown.
- Final boxed answer and commentary on common pitfalls.
- Where relevant, physical interpretation and check of units.
- Worked examples include both analytical solutions and numeric approximations.
- Cross-references to similar problems and topics for systematic practice.
- Summary exercises at chapter end with brief answers; full solutions for all 1,001 problems included in solution section.
Supplementary Material
- Appendix with mathematical tables and identities (integrals, transforms, series).
- Quick-reference formula sheets for exams.
- Answer index by topic and problem number for targeted practice.
- Problem difficulty index and estimated solving time per problem.
- Suggested study plans: 30-day, 12-week, and semester-long schedules.
- Instructor resources: suggested assignments, exam problems, and solution keys.
Examples of Representative Problems (sample, concise)
- Evaluate ∫_0^∞ x^2 e^-ax dx, a>0. (Solution uses Gamma function; result 2!/a^3 = 2/a^3.)
- Solve y'' + 4y = sin(2x) with initial conditions y(0)=0, y'(0)=1. (Method of undetermined coefficients plus homogeneous solution.)
- Compute eigenvalues and eigenvectors of [[4,1],[1,3]]. (Characteristic polynomial, normalization.)
- Use Newton-Raphson to find root of f(x)=x^3-2x-5 starting at x0=2 (iterate until specified tolerance).
- Evaluate residue at a simple pole and compute ∮ f(z) dz over given contour.
Formats & Accessibility
- Print-ready paperback and hardcover editions (well-indexed).
- Fully searchable eBook (PDF/EPUB) with linked cross-references.
- Companion website with downloadable problem sets, extra practice, and errata.
- Optional interactive solutions: stepwise reveal and numerical checkers.
- Accessible figures and high-contrast typesetting for readability.
Use Cases
- Primary course supplement for engineering mathematics, differential equations, linear algebra.
- Rapid review for competitive exams and technical interviews.
- Reference for practicing engineers needing worked examples for modelling tasks.
Estimated Page Count & Size
- ~700–900 pages depending on solution detail and appendices.
Marketing Blurb (concise)
- "1,001 fully worked problems across core engineering mathematics—your complete hands-on guide to mastering problem solving, from fundamentals to advanced applications."
If you want, I can:
- produce a detailed table of contents with approximate problem counts per chapter,
- generate 10 sample fully-worked problems and solutions from a chosen topic,
- or draft a 1-week study plan using problems from specific chapters. Which would you like?
1001 Solved Problems in Engineering Mathematics Excel Academic Council
(authored by Jaime R. Tiong and Romeo A. Rojas Jr.) is a comprehensive review guide widely used for engineering board exams like the ECE, CE, and ME licensure exams. It is structured as a 23-day review program
, organized by topics ranging from basic algebra to advanced mathematics. Structure and Content
The guide is designed for high-speed scannability and daily practice. Each "Day" typically includes a
section with summarized formulas and concepts, followed by a Multiple-choice test with an answer key and complete solutions. Review Day Core Topics Covered Systems of Numbers, Conversions, Real & Imaginary Numbers
Fundamentals of Algebra, Equations, Remainder & Factor Theorems Quadratic Equations, Binomial Theorem, Logarithms Age, Work, Mixture, Digit, and Motion Problems
Clock, Variation, Progression, and Miscellaneous Word Problems Venn Diagrams, Permutations, Combinations, and Probability Plane Geometry, Solid Mensuration, and Trigonometry Analytic Geometry (Parabola, Ellipse, Hyperbola) Differential and Integral Calculus, Differential Equations Key Features for Better Preparation Summarized Theory
: Provides quick access to essential formulas, "Tips & Trivia," and definitions like real vs. imaginary numbers. Timed Practice
: Each test specifies a target duration (e.g., 60 problems for 2 hours) to help you build speed for actual board exams. Complete Solutions
: Every problem has a step-by-step solution, making it ideal for self-paced learning. Supplemental Resources : Students often use GTR Math Tutorial on YouTube
which has video solutions specifically for this book's problem sets. Recommended Usage Strategy Follow the Day-by-Day Schedule
: Treat the 23-day structure as a strict curriculum to ensure you cover all engineering math subjects. Theory First
: Review the "Tips & Trivia" and summarized formulas before attempting the problems. Simulate Exam Conditions
: Time yourself for each practice test to improve your problem-solving efficiency. Cross-Reference
: For complex topics like calculus or fluid mechanics, supplement with texts from authors like Gillesania Are you preparing for a specific engineering board exam , or would you like to see a solved example for a particular topic like Word Problems or Calculus? 1001 Solved Problems in Engineering Math | PDF - Scribd 1001 Solved Problems in Engineering Mathematics , published
Mastering the Numbers: Why "1001 Solved Problems in Engineering Mathematics" is an Essential for Board Exam Success
For engineering students, particularly those in the Philippines, the name Excel Academic Council
is synonymous with intensive board exam preparation. Their cornerstone publication, 1001 Solved Problems in Engineering Mathematics
, authored by Jaime R. Tiong and Romeo A. Rojas Jr., has long served as a primary reference for reviewees across all disciplines—Civil, Electrical, Mechanical, Chemical, and Electronics Engineering. Comprehensive Coverage for Licensure Examinations
The book is meticulously structured to guide students through the vast landscape of engineering mathematics over a 23-day intensive schedule. Its curriculum covers: Fundamental Algebra: Number systems, logarithms, and binomial theorems. Applied Mathematics: Mixture, work, motion, and age problems. Advanced Geometry & Trigonometry:
Plane and solid geometry, analytic geometry (parabolas, ellipses, hyperbolas), and trigonometric identities. Calculus & Higher Math:
Differential and integral calculus, differential equations, and probability/statistics. Key Features for Efficient Review
What sets this collection apart from standard textbooks is its focus on high-speed, high-accuracy problem-solving required for licensure exams: Condensed Theory:
Each section begins with summarized formulas, concepts, and "Tips & Trivia" to refresh the user's memory without the fluff. Multiple-Choice Practice:
The problems are presented in a format that mirrors actual board exams, complete with an answer key for self-assessment. Complete Solutions:
Unlike many practice sets, every problem includes a step-by-step solution, which is crucial for students trying to understand complex derivation or shortcut methods. Calculator Techniques:
The book often incorporates specific techniques for scientific calculators, a vital skill for managing the time constraints of a professional board exam. The "Excel" Advantage
Under the leadership of Jaime R. Tiong, a 1st placer in the PICE National Students’ Quiz and president of the Excel First Review and Training Center, the Excel Academic Council has refined these 1,001 problems to represent the most frequently tested topics in licensure examinations. This targeted approach allows students to identify recurring problem types and master the specific logic used by board examiners.
Whether you are a student starting your engineering journey or a graduate in the thick of review season, this book remains a definitive resource for turning mathematical theory into practical, exam-ready expertise. 1001 Solved Problems in Engineering Maths | PDF - Scribd
1001 Solved Problems in Engineering Mathematics by Excel Academic Council has become a cornerstone resource for students and professionals across the Philippines preparing for board exams and technical coursework. Published by the Excel Review Center, this comprehensive guide bridges the gap between theoretical mathematical concepts and their practical applications in various engineering disciplines. Comprehensive Coverage of Engineering Math
The book is structured to guide learners through a logical progression of topics, moving from fundamental algebraic principles to advanced calculus and differential equations. Key subject areas include:
Algebra & Fundamentals: System of numbers, conversions, quadratic equations, binomial theorem, and logarithms.
Specialized Math Problems: Clock problems, variations, progressions (arithmetic and geometric), and Diophantine equations.
Probability & Statistics: Venn diagrams, permutations, combinations, and binomial distribution.
Geometry & Trigonometry: Plane geometry basics, area formulas, and complex trigonometric identities.
Advanced Engineering Math: Differential and integral calculus, differential equations, and vector analysis. Key Features for Board Exam Preparation Case Study: Passing the Board Exam with 1001
What sets this collection apart from standard textbooks is its focus on step-by-step problem-solving. Each of the 1,001 problems is presented with clear, detailed solutions that allow students to understand the underlying logic rather than just memorizing formulas.
Assessment of "1001 Solved Problems in Engineering Mathematics" by Excel Academic Council AbstractThe " 1001 Solved Problems in Engineering Mathematics
," published by the Excel Academic Council, serves as a cornerstone for engineering board exam preparation. Authors Jaime R. Tiong and Romeo A. Rojas, Jr. structured the text as a comprehensive workbook that emphasizes practical application over abstract theory. This paper evaluates the book’s pedagogical structure, thematic coverage, and its significance in contemporary engineering education. 1. Pedagogical Structure and Methodology
The book is distinct for its "Day-by-Day" structure, which organizes complex mathematical concepts into digestible, daily study modules. This systematic approach includes:
Step-by-Step Solutions: Each of the 1,001 problems is accompanied by a thorough explanation of the techniques used, making it accessible even to students who struggle with abstract concepts.
Calculator Techniques: A key feature noted by reviewers from the CE Board Exam Community is the inclusion of alternative solutions utilizing calculator short-cuts, which are critical for timed board examinations.
Progression of Difficulty: Problems begin with foundational concepts—such as the system of numbers—and escalate to advanced applications like Laplace transforms and differential equations. 2. Thematic Coverage
The text covers the full spectrum of engineering mathematics required for licensure exams. Key sections identified on Scribd include:
Day 1–5: Number systems, fundamentals of algebra, quadratic equations, and word problems (age, work, and mixture).
Day 6–10: Combinatorics, probability, Venn diagrams, and geometry (plane, solid, and spherical).
Day 11–14: Analytic geometry (conic sections) and differential calculus (limits, derivatives, and maxima/minima).
Day 15–20: Integral calculus, differential equations, and advanced engineering mathematics (matrices and Laplace transforms).
Day 21–23: Related engineering sciences, including strength of materials, dynamics, and engineering economy (annuities and depreciation). 3. Significance in Exam Preparation
The book 1001 Solved Problems in Engineering Mathematics by the Excel Academic Council (often authored by Jaime R. Tiong and Romeo A. Rojas Jr.) is a staple for engineering students, particularly those preparing for licensure board exams. Key Features & Content
The book is specifically designed to bridge the gap between theoretical knowledge and practical application through a structured, high-volume practice approach.
Structured Study Plan: The content is organized into a 23-day review format, making it easy for students to pace their preparation.
Comprehensive Coverage: It covers a vast range of engineering math subjects, including: Algebra: Number systems, binomial theorem, and logarithms.
Advanced Math: Differential and integral calculus, differential equations, and complex analysis.
Applied Topics: Probability, statistics, and some physics/engineering science subjects.
Problem Format: Each section typically includes summarized formulas and concepts, followed by multiple-choice questions (MCQs) with an answer key and complete, step-by-step solutions.
Step B – Topic‑by‑Topic Attack
Do not solve randomly. Follow this cycle per chapter: Differential Calculus: If you master the 40 time-rate
- Scan 5–10 problems – Identify which formulas are needed.
- Attempt closed‑book – Simulate exam conditions (time yourself: 2–3 minutes per easy problem, 5–7 for hard).
- Check answer only – If wrong, re‑attempt before reading the solution.
- Read the solution – Compare your method. Note their shortcuts.
- Mark problems:
- ✅ = correct first try
- ⚠️ = correct but slow
- ❌ = wrong or skipped