Numerical Analysis and Calculus of Several Variables
6H3714
Required reading:
Part 1: Calculus, A Complete Course; Adams, Robert A; edition 6 (or 5) ; Addison Wesley ; ISBN: 321270002:
Part 2:
1. Calculus, A Complete Course; Adams, Robert A; edition 6 (or 5) ; Addison Wesley ; ISBN: 321270002:
2. Differential Equations with Boundary-Value Problems, Denis G. Zill , Michael R Cullen,THOMSON LEARNING, edition 6 ( or 5) ISBN: 0534418872
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Recommended reading and exercises:
Part1: Calculus of several variables:
Calculus, R A. Adams, edeition 6 (or 5) / Recommended exercises:1 / Functions of Several Variables: Domain. Level Curves. / 12.1
/ 12.1 1-4, 11-16, 20
2 / Partial Derivatives. Normal Vector and Tangent Plane. / 12.3 / 12.3 1-8, 13,15,16, 25-31
3 / Higher-Order Derivatives. The Chain Rule.
Differentials. Taylor’s Formula and Approximations. / 12.4, 12.5
12.6 12.9 / 12.4 1-4, 10,11
12.5 9,1112.6 3,
12.9, 5
4 / Gradients and Directional Derivatives. Gradient, Divergence and Curl. / 12.7, 16.1 / 12.7 1,3,5
16.1 1-7
5 / Extreme Values. Classifying. Critical Points. / 13.1, 13.2 / 13.1 1-5
13.2 1-3
6 / Double integrals. Volumes. / 14.1-14.2 / 14.1 13,14
14.2 1-7
7 / Change of Variables in Double Integrals. Area of a Surface. / 14.4 14.7 / 14.4 1,3,5,7,9 14.7 1, 5,7
8 / Triple Integrals. / 14.5, 14.6 / 14.5 1-3 14.6 15
9 / Conservative Fields. Line Integrals of Vector Fields / 15.2, 15.3 / 15.2 1,2
15.4 1,3,5,7
10 / Flux Integrals / 15.6 / 15.6 1,3,5
Textbooks for part 2. The material in this part of the course is taken from many sources; particular references will be given in the lectures.
The following books are recommended but not obligatory for part 2.
Part 2:
1. Calculus, A Complete Course; Adams, Robert A; edition 6 (or 5) ; Addison Wesley ; ISBN: 321270002:
2. Differential Equations with Boundary-Value Problems, Denis G. Zill , Michael R Cullen,THOMSON LEARNING, edition 6 ( or 5) ISBN: 0534418872
Par2 : Numerical Analysis
Recommended exercises:1 /
Non-linear Equations.
Solving an Equation by Bisection.
Fixed-Point Iteration.
The secant method (Regula falsi).
The Newton-Raphson method.
/ Course material will be handed out during the lessons
+
Calculus, Adams: 4.6 / Handouts
CA;4.6 Examples 1, 2,3
CA;6.6 Exercises 1,3,5
2 / Systems of Linear and Nonlinear Equations. / Calculus, Adams: 13.6
+ Handouts / Handouts
CA;13.6 Example 1
Exercises 1,3,5
3 / Approximations. Taylor’s formula.
Polynomial Interpolation.
Lagrange’s Interpolations Formula / Calculus, Adams: 4.7, 4.8
+ Handouts / CA;4.7 Example 1
CA;4.8 Examples 1, 2, 5
4 / Cubic spline interpolation.
Numerical Differentiation
Numerical Integration.
The Trapezoidal and Midpoint Rules.
Simpson’s Rule. Approximate Integration Using Taylor formula / Calculus, Adams:
6.6, 6.7, 6.8 / CA;6.6 Examples 1,2,3
CA;6.6 Exercises 1,3
CA;6.7 Examples 1,2,3
6.7 Exercises 1,3
6.8 Example 4
5 / Numerical Treatment of Initial Value Problems for Ordinary Differential Equations.
Euler’s Method. Euler’s Method. The Fourth-Order Runge-Kutta Method. / Calculus Adams:
17.3 / CA;17.3Examples 1,2,3,4
CA;17.3 Exercises 1,3, 5
6 / Boundary Value Problems for Ordinary Differential Equations. Finite-Difference method / Diff Eq, Zill :
9.5 / Diff Eq; 9.5,
Examples 1,2
Exercises 3,5,7
7 / Boundary Value Problems for Partial Differential Equations. Finite-Difference method. Finite-Volume method. / Handouts
8 / Periodic Functions. Orthogonallity. Even and Odd Functions. Trigonometric Fourier series / Diff.Eq. Zill: 11.1, 11.2
Alternative: Calculus, 9.9: Exercises 1..5 / 11.1: 1,3
11.2: 1,3,7,9
9 / Cosine and Sine Series. / Diff.Eq. Zill: 11.3 / 11.3: 1,3,5, 7, 11,13
10 / Fourier Method for Ordinary and Partial Differential Equations. / Handouts+
Diff.Eq. Zill: 12.5
12.6 / 12.5 Exercise 7
12.6 Example 2