工程數學（二）

Class goal: To empower your ability to apply mathematics in real-world engineering problems and job situations. This is the second half of Engineering Mathematics designed to be a full academic year course. This course is to establish the fundamental mathematical knowledge for sophomore mechanical engineering students. This course will cover: Linear Algebra, Eigenvalue Problems, Vector Differential Calculus, Vector Integral Calculus, Fourier Analysis and PDE's.

Calculus and Engineering Math 1.

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Objective: Empowering you to apply mathematics to real-world engineering problems and job situations. Expectations: • You should aim to join every class. Any information you missed due to unannounced absence will be considered your loss. • Arrive to class on time and to stay for the entire class period (or until dismissed) because random arrivals and exits are disrespectful and distracting. This includes online classes (late-comer will not be admitted into class). • Supporting course materials will mostly be available on e3 including, lecture notes. Class will be taught at reasonable English level. Be prepared to also take notes during class. • All cell phones, smartphones, and other electronic devices (e.g., pagers, iPods) must be turned off (or on vibrate) and hidden from view during class time. • Laptop and tablet computers are allowed for (quiet) note taking only: i.e., other activities such as checking personal e-mail or browsing the Internet are prohibited. • Prepare for each class meeting and participate actively in discussion and activities. • Only projects will be graded. Suggested homework questions are to be completed on own volition and are not graded. Solutions will be provided. All late submissions will not be accepted without prior notice. • Be respectful of the views of other students.

• 20 % Midterm 1 + Correction • 25 % Midterm 2 + Correction • 25 % Final Exam • 15 % Project 1 • 15 % Project 2 Projects: to be completed in a group of ≤ 4 students. Midterm/final exam format: o Section 1: 1 page, 1-sided A4 note sheet that will be graded. (10% of exam) o Section 2: Concepts and definitions problems. (~20%) o Section 3: Classical problems. (~30%) o Section 4: Application problems. (~40%) o Correction (midterm only): Students can gain +10pt in exam. Corrections are held on the 1hr class session after midterm. Unless otherwise stated. o No make-up exams will be given. You are expected to structure your schedule to make it to the exams.

• Linear Algebra: Matrix Eigenvalue Problems

  Eigenvalues, Eigenvectors, applications, symmetric, skew-symmetric, orthogonal matrices. Eigenbases, diagnonalization, quadratic form.

• Vector Differential Calculus. Grad. Div. Curl.

  Vector and scalar functions and fields. Curves, arc length, curvature, torsion. Gradient of a scalar field, directional derivative. Divergence of a vector field. Curl of a vector field.

• Vector Integral Calculus. Integral Theorems

  Line integrals. Path independence of line integrals. Green's Theorem in the plane. Surfaces for surface integrals. Triple integrals, divergence theorem of Gauss.

• Fourier Series, Integrals and Transforms.

  Fourier Series, Fourier Integral, Fourier Transform, FFT, convolution.

• Partial Differential Equations.

  Basic concepts, modeling: vibrating strings and wave equations, solution by separation of variables and Fourier Series. D'Alembert's solution. Heat equation.

• Linear Algebra: Matrices, Vectors, Determinants. Linear Systems

  Matrix and vector operations, linear systems of equations, Gauss elimination, linear independence and rank, solutions, existence, uniqueness, Cramer's Rule, inverse

Advanced Engineering Mathematics by Erwin Kreyszig + supplemental notes.

地點

EE454

時間

By appointment.

聯絡方式

Instructor: 陈竺博渊 'Tanzu' (tanzu@nctu.edu.tw)