Engineering Mathematics with MATLAB® (Chul Ki Song Jong-Ryeol Kim)（Z-Library）

# Engineering Mathematics with MATLAB® — Reading Guide ## 【One-Line Pitch】 A streamlined, two-semester engineering mathematics textbook that pairs concise theoretical explanations with MATLAB®-based examples and visualization, ideal for undergraduate engineering students and instructors who want a practical, workload-manageable alternative to encyclopedic references. ## 【Book Arc】 - **Opening (~0%–14%)**: Front matter establishes the book's core philosophy—concise explanations, categorized key concepts, detailed solutions with alternative methods, and MATLAB® integration—along with author credentials and publisher information. The preface outlines eight design principles, including optional advanced topics and concept-focused exercises. - **Early (~14%–29%)**: Chapter 1 covers first-order ODEs, starting with fundamentals (definitions, initial value problems, differentiation/integration review), then progressing through separable equations, exact ODEs and integrating factors, Bernoulli equations (optional), and applications like Newton's law of cooling, radioactive decay, and electric circuits. Numerical methods (Euler, Runge-Kutta) and MATLAB® usage are introduced. - **Early–Middle (~29%–43%)**: Chapters 2–3 extend to second-order and higher-order ODEs, covering homogeneous equations with constant coefficients, Euler-Cauchy equations, undetermined coefficients, variation of parameters, and applications in vibration and electrical circuits. Chapter 4 introduces Laplace transforms, including s-shifting, t-shifting, unit step and Dirac delta functions, convolution, and system analysis. - **Middle (~43%–57%)**: Chapter 5 covers series solutions (power series and Frobenius methods) with Bessel functions and Legendre polynomials. Chapter 6 transitions to linear algebra—matrices, determinants, Gauss elimination, eigenvalues/eigenvectors—with applications in statics, vibration, and circuits. Chapter 7 connects linear algebra to systems of ODEs, including phase plane analysis (optional). - **Middle–Late (~57%–79%)**: Chapters 8–9 cover vector calculus (grad, div, curl; line, double, surface, and triple integrals; Green's, Gauss's, and Stokes's theorems). Chapter 10 introduces Fourier analysis (series, integrals, half-range expansions). Chapter 11 applies separation of variables to wave and heat equations in one and two dimensions. Chapters 12–13 conclude with complex numbers, analytic functions, Cauchy-Riemann equations, and complex integration including Cauchy's integral theorems. ## 【Key Takeaways】 - **Two-semester scope with deliberate pruning** (Early): The authors explicitly address the common problem of overstuffed engineering math textbooks by adjusting exercise counts and content depth to fit realistic academic schedules—a practical design choice for instructors. - **MATLAB® as a learning tool, not a black box** (Early): Each chapter includes a "Utilizing MATLAB®" section with worked examples (M_Example) that connect numerical computation to the analytical methods just taught, helping students verify results and visualize solutions. - **Categorized key concepts via "Remark" boxes** (Middle): Core principles are systematically organized under labeled remarks, making the material scannable for review and helping students distinguish essential ideas from supporting detail. - **Dual solution methods reinforce prior knowledge** (Middle): "Another Solution" sections deliberately connect new material back to high school calculus or earlier chapters, building continuity and offering alternative problem-solving strategies. - **Optional advanced topics marked clearly** (Late): Sections flagged (*optional)—such as Bernoulli equations, complex conjugate eigenvalues, phase planes, sound pressure equations, and Sturm-Liouville orthogonality—allow motivated students to go deeper without overwhelming the main flow. - **Applications span multiple engineering disciplines** (Late): Exercises and examples draw from mechanical (vibration, heat transfer), electrical (circuits, system analysis), and chemical engineering (mixing problems), grounding abstract methods in concrete physical contexts. - **Concept-focused exercises over calculation drills** (Late): The authors deliberately emphasize understanding over computational complexity, with problems organized by example type and difficulty kept consistent. ## 【Reading Tips】 - **Skim the front matter and preface** (~0%–14%): The preface's eight design principles tell you exactly how to use the book—look for "Remark," "Solution," "Another Solution," "Check," and "M_Example" boxes as you read. - **Deep-read the ODE chapters** (Early, ~14%–43%): These form the mathematical foundation for everything later. Pay special attention to the Laplace transform chapter—it's the bridge between ODEs and system analysis, and the t-shifting/Dirac delta material is often where students struggle. - **Use MATLAB® sections as verification tools** (throughout): Rather than reading them passively, try running the examples alongside your manual solutions. The "Utilizing MATLAB®" sections at each chapter's end are ideal for checking your work and building computational intuition. - **Treat optional sections as enrichment, not core** (throughout): If you're short on time, skip the (*optional) sections on first pass—they're self-contained and can be revisited later without breaking the main narrative. - **Watch for the linear algebra–ODE connection** (Middle, ~43%–57%): Chapter 6's eigenvalue material directly feeds Chapter 7's systems of ODEs. Don't treat these as separate topics; the eigenvector-based solutions in Chapter 7 are where linear algebra becomes practically indispensable. ## 【Coverage Limits】 The excerpts provide detailed chapter-level structure and pedagogical philosophy but do not include actual worked examples, exercise content, or MATLAB® code samples. Specific problem sets, figures, and numerical illustrations are not covered in this guide. ##