MATH2004 Notes - By Eric Hua
Contents
0.1. Fourier Series
3
0.2. Definition of Fourier Series.
4
0.3. Geometric interpretation of Fourier series.
8
0.4. Fourier cosine and Fourier sine series.
8
0.5. Convergence of Fourier Series.
11
0.6. Termwise differentiation and integration.
12
10.1. Curves Defined By Parametric Equations
13
10.2. Calculus with Parametric Equations
14
10.3. Polar Coordinates
17
10.4. Areas and Lengths in Polar Coordinates
20
12.1. Three-Dimensional Coordinate Systems
24
12.2. Vectors
24
12.3. The Dot Product
25
12.4. The Cross Product
26
12.5 Equations of Lines and Planes
27
12.6 Cylinders and Quadric Surfaces
29
13.1 Vector Functions and Space Curves
33
13.2 Derivatives and integrals of vector equations
34
13.3 Arc Length and Curvature
35
1
14.1. Functions of Several Variables
39
14.2. Limits and Continuity
39
14.3. Partial Derivatives
40
14.4. Tangent Plane and Linear Approximation
41
14.5. The Chain Rule
43
14.6. Directional Derivatives and the Gradient Vector
45
14.7. Maximum and Minimum Values
47
14.8. Lagrange Multipliers
50
15.1. Double Integrals over Rectangles
53
15.2. Iterated Integrals
53
15.3. Double Integrals over General Regions
54
15.4. Double Integrals in Polar Coordinates
56
15.7. Triple Integrals
15.7.1 Triple Integral over a Rectangular Box . . . . . . . . . . . . . . . . . . .
15.7.2 Triple Integrals over a General Region . . . . . . . . . . . . . . . . . . . .
57
57
58
15.8. Triple Integrals in Cylindrical Coordinates
60
15.9. Triple Integrals in Spherical Coordinates
62
16.1. Vector Fields
65
16.2. Line Integrals
65
16.3. The Fundamental Theorem for Line Integrals
68
16.4. Green’s Theorem
70
2
0.1. Fourier Series
Pre-knowledge
1. Trig Identities:
π
) = (−1)n ; cos(nπ ) = (−1)n , n...