math121a-f23:start

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 **

- 0. Some calculus and Linear algebra (review).
- 1. Complex analysis.
- 2. Integral transform (Fourier transformation).
- 3. Calculus of Variation.

** 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.

- For Linear Algebra, we had some suggestions
- Prof Paulin's Linear Algebra and Differential Equations (Math 54) Spring 2018 Videos and Lecture Notes (thanks to Adam for sharing)
- Essense of Linear algebra (thanks to Cameron for sharing)

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 |

math121a-f23/start.txt · Last modified: 2023/12/13 00:28 by pzhou