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
----------------------------------------------------------------------------------------------------------------
Recommended reading and exercises:
Part1: Calculus of several variables:
1 Functions of Several Variables: Domain.
Level Curves.
2 Partial Derivatives. Normal Vector and
Tangent Plane.
3 Higher-Order Derivatives. The Chain Rule.
Differentials. Taylor’s Formula and
Approximations.
4 Gradients and Directional Derivatives.
Gradient, Divergence and Curl.
5 Extreme Values. Classifying. Critical Points.
6 Double integrals. Volumes.
Calculus, R A.
Adams, edeition 6
(or 5)
12.1
Recommended
exercises:
12.3
12.3 1-8,
13,15,16, 25-31
12.4, 12.5
12.6 12.9
12.4 1-4, 10,11
12.5 9,1112.6 3,
12.9, 5
12.7, 16.1
12.7 1,3,5
16.1 1-7
13.1, 13.2
13.1 1-5
13.2 1-3
14.1 13,14
14.2 1-7
14.1-14.2
7 Change of Variables in Double Integrals. Area 14.4 14.7
of a Surface.
14.5, 14.6
8 Triple Integrals.
9 Conservative Fields. Line Integrals of Vector 15.2, 15.3
Fields
15.6
10 Flux Integrals
12.1 1-4, 11-16,
20
14.4 1,3,5,7,9
14.7 1, 5,7
14.5 1-3 14.6 15
15.2 1,2
15.4 1,3,5,7
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
1
Non-linear Equations.
Solving an Equation by Bisection.
Fixed-Point Iteration.
The secant method (Regula falsi).
The Newton-Raphson method.
Recommended
exercises:
Course material will Handouts
be handed out
CA;4.6 Examples
during the lessons 1, 2,3
+
CA;6.6 Exercises
Calculus, Adams:
1,3,5
4.6
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.
Calculus, Adams:
4.7, 4.8
+ Handouts
CA;4.7 Example 1
CA;4.8 Examples
1, 2, 5
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
CA;17.3Examples
1,2,3,4
CA;17.3
Exercises 1,3, 5
Polynomial Interpolation.
Lagrange’s Interpolations Formula
4 Cubic spline interpolation.
Numerical Differentiation
Numerical Integration.
The Trapezoidal and Midpoint Rules.
Simpson’s Rule. Approximate Integration
Using Taylor formula
5 Numerical Treatment of Initial Value Problems for
6
Calculus Adams:
17.3
Ordinary Differential Equations.
Euler’s Method. Euler’s Method. The Fourth-Order
Runge-Kutta Method.
Boundary Value Problems for Ordinary Differential Diff Eq, Zill :
9.5
Equations. Finite-Difference method
7 Boundary Value Problems for Partial Differential
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
Diff.Eq. Zill: 11.3
Diff Eq; 9.5,
Examples 1,2
Exercises 3,5,7
Equations. Finite-Difference method. FiniteVolume method.
9 Cosine and Sine Series.
10 Fourier Method for Ordinary and Partial
Differential Equations.
Handouts+
Diff.Eq. Zill: 12.5
12.6
11.1: 1,3
11.2: 1,3,7,9
11.3: 1,3,5, 7,
11,13
12.5 Exercise 7
12.6 Example 2