Week1: Read Ch 1 throroughly, Except 1.2.5 and 1.3.11 can be read cursorly. Practice with some of the review questions (p. 39) until you are comfortable with the content. Do for yourself Exercise 1.2, 1.4, 1.5, 1.9, 2.4, 2.7, 2.10 To prepare for the next week lectures, read through: 2.1, 2.4-2.4.8. (We will first do the practical "how to" solve linear systems, then later revisit the mathematical properties in 2.2 and 2.3.) Week 2: Read Ch 2.2 and 2.3. Particularly pay attention to the error bounds (Ch 2.3.4 and fig 2.4) Then explore systems with different conditioning yourself using this on-line calculator Compare your results with fig 2.4. Read through cursorly the rest of Ch 2.4.9-2.7. Do review questions. Suggested exercises: (p 97-98) 2.8a, 2.12, 2.22, 2.25 Computer problems: (p. 100) 2.3, 2.10 To prepare for next week read through: 3.1-3.4, Skim 3.5 Week 3 and 6: Read Ch 3 to 3.7. Then try this demo on polynomial data fitting Suggested exercises: 3.1, 3.5, 3.16 Computer problems: 3.2, 3.5, 3.8 Week 4: In detail: 7.1-7.3.3, to p. 319. Medium detail: 7.4 Try comparing poly's and splines Skim rest of Ch 7. Suggested exercises: 7.1 7.2 7.4, 7.15 Computer problems: 7.3, 7.5, 7.8 Week 5-6: Review math125 topics as needed 4.1-4.2.4, Read cursorly until 4.4.1 In detail 4.5.1,2 demo, Medium detail: 4.5.5 Simultaneous iteration Cursorly: rest of 4.5, 4.6. Try to get the gist of QR iteration. Detail: 3.6 SVD. More info and applications on SVD Suggested exercises: 4.1, 4.3, 4.12, 4.16, 4.24, 3.30, 3.31 Computer problems: 4.2, 4.5, 4.12 Week 6: Review of material, examples and exercises in preparation for the exam. Tue: Midterm. Thu: More on Ch 3, 4 methods. Orthogonality, Gram-Schmidt, Givens transforms Week 7-8: Read Ch 5. except can just skim 5.5.5-5.5.6 Try the demos on fixed point iteration and Newton's method Suggested exercises: 5.1, 5.2, 5.4, 5.9 Computer problems: 5.2, 5.3 Week 9: Read Ch 6.1-6.6 In detail: 6.5.3 and 6.6.1 Try the demos of Golden section search, Newton's 1D method,Newton's n-D and Steepest Descent. Suggested exercises: 6.1a,b, 6.2a,b, 6.3a,b, 6.9 Computer problems: 6.2, 6.5, 6.15 Week 10: Read Ch 8.1, 8.3.1, 8.3.5, 8.6, 8.7, Rest of Ch 8 cursorly Try demos on derivatives, Newton-Cotes quadrature, Romberg integration. Suggested exercises: 8.2, 8.11, 8.12 Computer problems: 8.1, 8.18 Week 11: Selected topics TBA Last weeks: Review and exercises in preparation for exam 2.
Linear Equations NR Ch 2,15.1-4,3,11, Heath Ch 2,3,7,4. Linear equations, geometry and matrix factorizations
Nonlinear Equations and Optimization NR Ch 9,10,15.5 Heath Ch 5,6. Nonlinear systems and applications in kinematics
Numerical Integration and Differentiation NR Ch 4, Heath Ch 8. Lecture material
Selected CS topics and Applications: NR Ch 12, Heath Ch 12, 13.1
Heath provides a numerical and mathematical in-depth treatment of the course topics. This book is the best course text for those interested in mathematical depth.
A standard reference for scientists and engineers, Numerical Recipes contains both methods and algorithms implemented in C. While a handy reference it is however somewhat of a compromise as a textbook.