|
Simple Calculations with MATLAB |
|
|
1 | (26) |
|
Introduction and a Word of Warning |
|
|
1 | (1) |
|
Scalar Quantities and Variables |
|
|
2 | (10) |
|
Rules for Naming of Variables |
|
|
4 | (1) |
|
Precedence: The Order in Which Calculations Are Performed |
|
|
5 | (3) |
|
|
8 | (4) |
|
Format: The Way in Which Numbers Appear |
|
|
12 | (1) |
|
|
13 | (4) |
|
Initialising Vector Objects |
|
|
13 | (1) |
|
Manipulating Vectors and Dot Arithmetic |
|
|
14 | (3) |
|
Setting Up Mathematical Functions |
|
|
17 | (3) |
|
Some MATLAB Specific Commands |
|
|
20 | (3) |
|
Looking at Variables and Their Sizes |
|
|
22 | (1) |
|
Accessing Elements of Arrays |
|
|
23 | (1) |
|
|
24 | (3) |
|
Writing Scripts and Functions |
|
|
27 | (36) |
|
Creating Scripts and Functions |
|
|
27 | (9) |
|
|
30 | (5) |
|
|
35 | (1) |
|
Plotting Simple Functions |
|
|
36 | (13) |
|
Evaluating Polynomials and Plotting Curves |
|
|
41 | (3) |
|
|
44 | (5) |
|
|
49 | (2) |
|
|
51 | (6) |
|
|
51 | (3) |
|
|
54 | (3) |
|
|
57 | (6) |
|
Loops and Conditional Statements |
|
|
63 | (40) |
|
|
63 | (1) |
|
|
63 | (5) |
|
|
68 | (15) |
|
Sums of Series of the Form NΣ j=4 jp, p ε N |
|
|
73 | (3) |
|
|
76 | (3) |
|
Summing Series Using MATLAB Specific Commands |
|
|
79 | (3) |
|
Loops Within Loops (Nested) |
|
|
82 | (1) |
|
|
83 | (7) |
|
Constructing Logical Statements |
|
|
85 | (3) |
|
The MATLAB Command switch |
|
|
88 | (2) |
|
|
90 | (2) |
|
|
92 | (1) |
|
|
92 | (2) |
|
|
94 | (3) |
|
|
97 | (6) |
|
|
103 | (30) |
|
|
103 | (1) |
|
|
104 | (5) |
|
|
109 | (4) |
|
|
113 | (4) |
|
Newton--Raphson and Secant Methods |
|
|
117 | (6) |
|
Derivation of the Newton--Raphson Method |
|
|
117 | (6) |
|
Repeated Roots of Functions |
|
|
123 | (2) |
|
Zeros of Higher-Dimensional Functions(*) |
|
|
125 | (3) |
|
MATLAB Routines for Finding Zeros |
|
|
128 | (2) |
|
|
128 | (1) |
|
|
128 | (2) |
|
|
130 | (3) |
|
Interpolation and Extrapolation |
|
|
133 | (36) |
|
|
133 | (1) |
|
|
134 | (5) |
|
|
139 | (2) |
|
Newton Forward Differences and Lagrange Polynomials |
|
|
141 | (7) |
|
Linear Interpolation/Extrapolation |
|
|
147 | (1) |
|
Calculating Interpolated and Extrapolated Values |
|
|
148 | (2) |
|
|
150 | (2) |
|
|
152 | (3) |
|
Interpolation of Non-Smooth Data |
|
|
155 | (6) |
|
|
158 | (3) |
|
Minimisation of Functions and Parameter Retrieval |
|
|
161 | (5) |
|
|
163 | (1) |
|
Using fmins for Parameter Retrieval |
|
|
164 | (2) |
|
|
166 | (3) |
|
|
169 | (56) |
|
|
169 | (17) |
|
Initialising Matrices Within MATLAB |
|
|
169 | (5) |
|
|
174 | (6) |
|
Operations on Elements of Matrices |
|
|
180 | (2) |
|
|
182 | (3) |
|
Matrices Containing Strings |
|
|
185 | (1) |
|
Properties of Matrices and Systems of Equations |
|
|
186 | (5) |
|
|
190 | (1) |
|
Elementary Row Operations |
|
|
191 | (8) |
|
Solving Many Equations at Once |
|
|
198 | (1) |
|
|
199 | (5) |
|
Eigenvalues and Eigenvectors |
|
|
204 | (4) |
|
|
208 | (4) |
|
Characteristic Polynomials |
|
|
212 | (2) |
|
|
214 | (3) |
|
|
217 | (8) |
|
|
225 | (22) |
|
|
225 | (1) |
|
Integration Using Straight Lines |
|
|
226 | (4) |
|
Errors in the Trapezium Method |
|
|
229 | (1) |
|
Integration Using Quadratics |
|
|
230 | (5) |
|
Integration Using Cubic Polynomials |
|
|
235 | (2) |
|
Integrating Using MATLAB Commands |
|
|
237 | (1) |
|
Specific Examples of Integrals |
|
|
238 | (4) |
|
Infinite Integrals and Removable Singularities |
|
|
238 | (2) |
|
|
240 | (2) |
|
|
242 | (5) |
|
Solving Differential Equations |
|
|
247 | (44) |
|
|
247 | (1) |
|
Euler's Method and Crank--Nicolson |
|
|
247 | (12) |
|
|
253 | (6) |
|
|
259 | (4) |
|
|
263 | (3) |
|
|
266 | (12) |
|
|
266 | (4) |
|
|
270 | (3) |
|
|
273 | (1) |
|
|
274 | (4) |
|
|
278 | (4) |
|
|
282 | (3) |
|
Eigenvalues of Differential Systems |
|
|
285 | (1) |
|
|
286 | (5) |
|
Simulations and Random Numbers |
|
|
291 | (32) |
|
|
291 | (1) |
|
|
291 | (4) |
|
|
291 | (2) |
|
Other Statistical Measures |
|
|
293 | (2) |
|
Random Numbers and Distributions |
|
|
295 | (5) |
|
|
298 | (1) |
|
Calculating Probabilities |
|
|
299 | (1) |
|
|
300 | (1) |
|
|
300 | (19) |
|
Modelling Discrete Systems |
|
|
307 | (2) |
|
|
309 | (7) |
|
|
316 | (3) |
|
|
319 | (4) |
|
A. Mathematical Introduction to Matrices |
|
|
323 | (12) |
|
|
330 | (1) |
|
|
331 | (4) |
|
B. Glossary of Useful Terms |
|
|
335 | (54) |
|
Arithmetic and Logical Operators |
|
|
335 | (8) |
|
|
343 | (4) |
|
|
347 | (18) |
|
|
365 | (24) |
|
|
389 | (70) |
|
Solutions for Tasks from Chapter 1 |
|
|
389 | (5) |
|
Solutions for Tasks from Chapter 2 |
|
|
394 | (6) |
|
Solutions for Tasks from Chapter 3 |
|
|
400 | (8) |
|
Solutions for Tasks from Chapter 4 |
|
|
408 | (6) |
|
Solutions for Tasks from Chapter 5 |
|
|
414 | (4) |
|
Solutions for Tasks from Chapter 6 |
|
|
418 | (11) |
|
Solutions for Tasks from Chapter 7 |
|
|
429 | (7) |
|
Solutions for Tasks from Chapter 8 |
|
|
436 | (18) |
|
Solutions for Tasks from Chapter 9 |
|
|
454 | (5) |
Index |
|
459 | |