工程數學(2)

(中) 本課程將介紹工程數學的基本觀念,並教授學生如何利用應用相關知識解決工程問題。 (Eng.) This course will introduce some basic concepts of engineering mathematics, and teach students how to apply relevant knowledge to solve engineering problems.

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作業、出席、學習態度:10%。 學習測驗:90% (3 Tests, each 30%)。 出席與學習態度(酌量加分)。

• Chap-8, Linear Algebra: Matrix Eigenvalue Problems,

  a. The Matrix Eigenvalue Problem, Determining Eigenvalues and Eigenvectors, b. Some Applications of Eigenvalue Problems, Symmetric, Skew- c. Symmetric, and Orthogonal Matrices, d. Eigenbases. Diagonalization. Quadratic Forms, e. Complex Matrices and Forms. Optional

  講授：

  9

• Chap-9, Vector Differential Calculus, Grad, Div, Curl,

  a. Vectors in 2-Space and 3-Space, b. Inner Product (Dot Product), c. Vector Product (Cross Product), d. Vector and Scalar Functions and Their Fields. Vector Calculus: Derivatives, e. Curves. Arc Length. Curvature. Torsion, f. Calculus Review: Functions of Several Variables. Optional, g. Gradient of a Scalar Field. Directional Derivative, h. Divergence of a Vector Field, i. Curl of a Vector Field

  講授：

  9

• Chap-10, Vector Integral Calculus, Integral Theorems,

  a. Line Integrals, b. Path Independence of Line Integrals, c. Calculus Review: Double Integrals. Optional, d. Green’s Theorem in the Plane, e. Surfaces for Surface Integrals, f. Surface Integrals, g. Triple Integrals. Divergence Theorem of Gauss, h. Further Applications of the Divergence Theorem, i. Stokes’s Theorem

  講授：

  9

• Chap-11,Fourier Analysis,

  a. Spillways b. Fourier Series, c. Arbitrary Period. Even and Odd Functions. Half-Range Expansions, d. Forced Oscillations, e. Approximation by Trigonometric Polynomials, f. Sturm–Liouville Problems. g. Orthogonal Function, Orthogonal Series. Generalized Fourier Series, h. Fourier Integral, i. Fourier Cosine and Sine Transforms, j. Fourier Transform. Discrete and Fast Fourier Transforms, k. Tables of Transforms

  講授：

  9

• Exams

  a. First Exam b. Second Exam c. Third Exam

  講授：

  9

• Chap-7, Linear Algebra: Matrices, Vectors, Determinants, Linear Systems,

  a. Matrices, Vectors: Addition and Scalar Multiplication, b. Matrix Multiplication, c. Linear Systems of Equations. Gauss Elimination, d. Linear Independence. Rank of a Matrix. Vector Space, e. Solutions of Linear Systems: Existence, Uniqueness, f. For Reference: Second- and Third-Order Determinants, g. Determinants. Cramer’s Rule h. Inverse of a Matrix. Gauss–Jordan Elimination, i. Vector Spaces, Inner Product Spaces. Linear Transformations. Optional

  講授：

  9

Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, Inc. 10th Edition, 2018.

地點

Department of Civil Engineering, Engineering Building (II), Room 309.

時間

Wednesday, 10:00~12:00

聯絡方式

03-5731917 dsshih@nctu.edu.tw