Solving Problems in Mathematical Analysis, Part III: Curves and Surfaces, Conditional Extremes, Curvilinear Integrals, Complex Functions, ... Fourier Series (Problem Books in Mathematics)

Preface
Contents
Definitions and Notation
1 Examining Curves and Surfaces
	1.1 Finding Curvature and Torsion of Curves
		Problem 1
		Solution
		Problem 2
		Solution
		Problem 3
		Solution
	1.2 Examining k-Surfaces in N Dimensions
		Problem 1
		Solution
		Problem 2
		Solution
		Problem 3
		Solution
		Problem 4
		Solution
	1.3 Examining Ruled Surfaces
		Problem 1
		Solution
		Problem 2
		Solution
		Problem 3
		Solution
		Problem 4
		Solution
	1.4 Exercises for Independent Work
2 Investigating Conditional Extremes
	2.1 Using the Method of the Lagrange Multipliers
		Problem 1
		Solution
		Problem 2
		Solution
		Problem 3
		Solution
		Problem 4
		Solution
	2.2 Looking for Global Extremes
		Problem 1
		Solution
		Problem 2
		Solution
		Problem 3
		Solution
	2.3 Exercises for Independent Work
3 Investigating Integrals with Parameters
	3.1 Examining Limits and Continuity
		Problem 1
		Solution
		Problem 2
		Solution
		Problem 3
		Solution
	3.2 Differentiating with Respect to Parameters
		Problem 1
		Solution
		Problem 2
		Solution
		Problem 3
		Solution
		Problem 4
		Solution
		Problem 5
		Solution
		Problem 6
		Solution
	3.3 Integrating over Parameters
		Problem 1
		Solution
		Problem 2
		Solution
	3.4 Exercises for Independent Work
4 Examining Unoriented Curvilinear Integrals
	4.1 Finding Area of Surfaces
		Problem 1
		Solution
		Problem 2
		Solution
		Problem 3
		Solution
	4.2 Calculating Various Curvilinear Integrals
		Problem 1
		Solution
		Problem 2
		Solution
		Problem 3
		Solution
	4.3 Exercises for Independent Work
5 Examining Differential Forms
	5.1 Studying the Exterior Forms Operating on Vectors
		Problem 1
		Solution
		Problem 2
		Solution
		Problem 3
		Solution
	5.2 Performing Various Operations on Differential Forms
		Problem 1
		Solution
		Problem 2
		Solution
		Problem 3
		Solution
		Problem 4
		Solution
		Problem 5
		Solution
	5.3 Calculating Exterior Derivatives
		Problem 1
		Solution
		Problem 2
		Solution
		Problem 3
		Solution
		Problem 4
		Solution
	5.4 Looking for Primitive Forms
		Problem 1
		Solution
		Problem 2
		Solution
		Problem 3
		Solution
		Problem 4
		Solution
		Problem 5
		Solution
	5.5 Finding Potentials in  R3
		Problem 1
		Solution
		Problem 2
		Solution
		Problem 3
		Solution
		Problem 4
		Solution
		Problem 5
		Solution
	5.6 Exercises for Independent Work
6 Examining Oriented Curvilinear Integrals
	6.1 Calculating Integrals over Curves
		Problem 1
		Solution
		Problem 2
		Solution
		Problem 3
		Solution
	6.2 Calculating Integrals over Surfaces
		Problem 1
		Solution
		Problem 2
		Solution
		Problem 3
		Solution
	6.3 Using Stokes' Theorem
		Problem 1
		Solution
		Problem 2
		Solution
		Problem 3
		Solution
		Problem 4
		Solution
		Problem 5
		Solution
		Problem 6
		Solution
	6.4 Exercises for Independent Work
7 Studying Functions of Complex Variable
	7.1 Examining the Holomorphicity of Functions
		Problem 1
		Solution
		Problem 2
		Solution
		Problem 3
		Solution
		Problem 4
		Solution
	7.2 Finding Domains of Convergence of Complex Series
		Problem 1
		Solution
		Problem 2
		Solution
		Problem 3
		Solution
	7.3 Calculating Contour Integrals
		Problem 1
		Solution
		Problem 2
		Solution
		Problem 3
		Solution
		Problem 4
		Solution
		Problem 5
		Solution
	7.4 Using Cauchy's Theorem
		Problem 1
		Solution
		Problem 2
		Solution
		Problem 3
		Solution
	7.5 Looking for Images of Sets
		Problem 1
		Solution
		Problem 2
		Solution
		Problem 3
		Solution
		Problem 4
		Solution
	7.6 Exercises for Independent Work
8 Investigating Singularities of Complex Functions
	8.1 Identifying the Types of Singularities
		Problem 1
		Solution
		Problem 2
		Solution
		Problem 3
		Solution
		Problem 4
		Solution
	8.2 Expanding Functions into Laurent Series
		Problem 1
		Solution
		Problem 2
		Solution
		Problem 3
		Solution
	8.3 Using the Residue Theorem to Calculate Definite Integrals
		Problem 1
		Solution
		Problem 2
		Solution
		Problem 3
		Solution
		Problem 4
		Solution
	8.4 Using Residue Theorem to Find Sums of Series
		Problem 1
		Solution
		Problem 2
		Solution
	8.5 Exercises for Independent Work
9 Dealing with Multivalued Functions
	9.1 Analytically Continuing Functions
		Problem 1
		Solution
		Problem 2
		Solution
		Problem 3
		Solution
		Problem 4
		Solution
	9.2 Calculating Integrals Involving Functions with Branch Points
		Problem 1
		Solution
		Problem 2
		Solution
		Problem 3
		Solution
		Problem 4
		Solution
		Problem 5
		Solution
		Problem 6
		Solution
		Problem 7
		Solution
		Problem 8
		Solution
	9.3 Exercises for Independent Work
10 Studying Fourier Series
	10.1 Examining Expandability of Functions into Fourier Series
		Problem 1
		Solution
		Problem 2
		Solution
	10.2 Finding Fourier Coefficients
		Problem 1
		Solution
		Problem 2
		Solution
		Problem 3
		Solution
		Problem 4
		Solution
		Problem 5
		Solution
	10.3 Exercises for Independent Work
Index