Berkeley Math 121A.
Lecture: MoWeFr 10:00AM - 10:59AM Dwinelle 109
Office Hour: Wednesday 11am-12:30noon, Friday 11am-12:30noon. Evans 753
Final Exam: Dec 11, 8-11am, classroom Dwinelle 109
online discussion : Discord
anonymous feedback : google form
Content
Grades Final (40%) + Midterms (20%) + Homework (40%)
Textbook The traditional textbook is Mathematical Methods in the Physical Sciences by Boas . But we will not follow this one closely. I will post reading materials here.
| Date (Day of Week) | Content |
| August 23 (Wednesday) | Introduction, What is math for physics? |
| August 25 (Friday) | Review of Linear algebra |
| Homework 1 | |
| August 28 (Monday) | Review of Linear algebra 2 |
| August 30 (Wednesday) | Review of Calculus, limit and series |
| September 1 (Friday) | Review of Calculus, differentiations and integral |
| Homework 2 | |
| September 6 (Wednesday) | Complex number, geometry of complex number |
| September 8 (Friday) | Basic complex functions. Log. poles |
| Homework 3 | |
| September 11 (Monday) | Analytic Function. Meromorphic Function. Series Expansion |
| September 13 (Wednesday) | Integral of holomorphic functions |
| September 15 (Friday) | Contour integral: Exercises |
| Homework 4 | |
| September 18 (Monday) | Residue Theorem and More Contour Integral |
| September 20 (Wednesday) | Riemann sphere. |
| September 22 (Friday) | Branch Cut, multivalued function |
| Homework 5 | |
| September 25 Monday | Application to real integrals. |
| September 27, Wednesday | Gaussian integral. Steepest Descent. |
| September 29 (Friday) | Review |
| No HW | |
| October 2 (Monday) | Midterm 1 |
| October 4 (Wednesday) | Fourier integral |
| October 6 (Friday) | Inverse transform, Fourier Series |
| Homework 6 | |
| October 9 (Monday) | Discrete Fourier Transform. Summary. |
| October 11 (Wednesday) | Examples of Fourier Transform. |
| October 13, Friday | Parseval Equality. Convolution. |
| Homework 7 | |
| October 16 (Monday) | Laplace Transform. |
| October 18 (Wednesday) | |
| October 20 (Friday) | Practice Day |
| Homework 8 | |
| October 23 (Monday) | Constant Coeff Diff Eq. Characteristic Eq. |
| October 25 (Wednesday) | general formula |
| October 27 (Friday) | Laplace method. Inhomogeneous term |
| HW 9 | |
| October 30 (Monday) | Delta function, Green's function |
| November 1 (Wednesday) | Other methods for solving ODE |
| November 3 (Friday) | Review video |
| November 6 (Monday) | Midterm 2 |
| November 8 (Wednesday) | midterm review, and Boas 8.2, 8.3 |
| November 10 (Friday) | no class |
| HW 10 (Due Nov 17) | Boas S8.2 #1,3,8, S8.3 #2, 5, 11 |
| November 13 (Monday) | review minimum |
| November 15 (Wednesday) | example of variation problem. Boas 9.1 video |
| November 17 (Friday) | Euler equation Boas 9.2 video |
| HW 11 (Due Nov 27) | Boas (9.1 #2,3 ), (9.2 # 1,2,3,9) |
| November 20 (Monday) | examplesvideo |
| November 27 (Monday) | optimize with constraints video |
| November 29 (Wednesday) | |
| December 1 (Friday) | |
| December 11 (Monday) | final,solution |