**Instructor**: Nikhil Srivastava, email: *firstname at math.berkeley.edu*

**Lectures**: MWF 9-10am, Cory Hall 289.

**Office Hours**: Monday 2-3, Tuesday 9-10, and Thursday 11-1, Evans Hall 1035.

**Text**: Mary L. Boas, *Mathematical Methods in the Physical Sciences, 3e.*

**Grading**: 30% Homework, 30% Midterms, 40% Final. The lower midterm score will be replaced by the final exam score, if it helps.

Homework will be assigned every Friday and due the following Friday at the end of class, except for the week of 3/20 (Midterm 2), when it will be due two days earlier on 3/18. Solutions will be posted on this page each Friday or early Saturday, and late homework will not be accepted. The two lowest homework grades will be dropped.

** Announcements **

- (2/11) HW4 will be assigned early on Wednesday, 2/11. It will *not* be collected, but solutions will be posted online on Monday, 2/16, so please do it before that. The material on HW4 will be included in the first midterm.
- (2/12) There will be extra office hours on Tuesday, 2/17, the day before the midterm.
- (2/12) The midterm is in-class and closed book: no notes, textbooks, etc.
- (2/14) Here is a sample midterm 1, as well as solutions.
- (2/14) Here are some extra practice problems for linear algebra: extra linear algebra problems.
- (2/20) New midterm grading policy: I will replace your lower midterm score with your final exam score, if it helps.
- (2/21) Here are the solutions to midterm 1.
- (3/9) Office hours for the week of March 9-13 will be: Tu 8-9, We 2-3, Th 8-9 and 1230-130.
- (3/9) Reminder: HW8 will be assigned early (3/11) and collected early (3/18).
- (3/15) Here is a sample midterm 2.
- (3/17) Here are the sample midterm 2 solutions
- (3/18) Here is a handout describing what you can cite on the midterm while calculating limits of integrals. It also includes some extra problems for practice.
- (4/3) Here are the midterm 2 solutions
- (4/14) HW10 is due on Monday, April 20.
- (5/4) A sample final with practice problems is up
- (5/7) Sample final solutions.

** Readings and Homework Schedule**

# | Date | Topic | Readings | HW | Notes |

1 | Jan 21 | Intro to series | 1.1-1.4 | ||

2 | Jan 23 | Tests for convergence | 1.5-1.9 | HW1 assigned | |

3 | Jan 26 | Power series | 1.10-1.13 | ||

4 | Jan 28 | Taylor series, error terms | 1.13-1.14 | ||

5 | Jan 30 | Asymptotic notation, applications of series | 1.15-1.16 + Lecture notes | HW2 assigned* HW1 Solutions posted | guest lecture by Marius Beceanu HW1 due |

6 | Feb 2 | Diagonalization, decoupling principle | Lecture notes on diagonalization | ||

7 | Feb 4 | More diagonalization, applications | 3.11-3.12 | ||

8 | Feb 6 | Spectral theorem, inner product spaces | 3.9, 3.14 | HW3 assigned HW2 Solutions posted | HW2 due |

9 | Feb 9 | Partial differentiation, chain rule | 4.1-4.5 | ||

10 | Feb 11 | More chain rule, gradients, max/min problems | 4.6-4.9 Lecture notes on chain rule | HW4 assigned | |

11 | Feb 13 | Max/min problems, Lagrange multipliers | 4.9-4.10 | HW3 Solutions posted | HW3 due |

Feb 16 | No class | HW4 Solutions posted | |||

12 | Feb 18 | Midterm 1 | |||

13 | Feb 20 | Complex numbers | 2.1-2.5 | HW5 assigned | |

14 | Feb 23 | Complex series, the exponential function, Euler's formula | 2.6-2.15 lecture notes | ||

15 | Feb 25 | Powers, roots, logarithm, trig functions | 2.11-2.15 | ||

16 | Feb 27 | Complex differentiation, Cauchy-Riemann equations | 14.1-14.2 | HW6 assigned HW5 solutions posted | |

17 | Mar 2 | Contour integration | 14.3 | ||

18 | Mar 4 | Cauchy's integral formula and consequences | 14.3 | ||

19 | Mar 6 | Laurent series | 14.4 | HW7 assigned HW6 solutions posted | |

20 | Mar 9 | Residue theorem | 14.5-14.6 Lecture notes on residue thm and Laurent Series | ||

21 | Mar 11 | Applications of residue calculus | 14.7 Lecture notes on Jordan's lemma and PV | HW8 assigned | |

22 | Mar 13 | Applications of residue calculus | 14.7 | HW7 solutions posted Grader's solutions | |

23 | Mar 16 | Integrating along a branch cut, Liouville's Thm, FTA | 14.7 | ||

24 | Mar 18 | Summing series using residues, review | HW8 solutions posted | ||

25 | Mar 20 | Midterm 2 | |||

26 | Mar 30 | Intro to Fourier series, heat equation | lecture notes, skim 7.1-7.7 | ||

27 | Apr 1 | Inner product space formulation, convergence in L2 | lecture notes | ||

28 | Apr 3 | More on L2 convergence | HW9 assigned | due April 14 at 5pm | |

29 | Apr 6 | Pointwise convergence, differentiation, even/odd functions | lecture notes | ||

30 | Apr 8 | The Fourier transform, Gaussians | lecture notes | ||

31 | Apr 10 | Properties of Fourier transforms, convolution | lecture notes | guest lecture by Marius Beceanu | |

32 | Apr 13 | More convolution, Poisson summation | lecture notes | HW10 assigned | Due April 20 at 5pm |

33 | Apr 15 | Delta functions | 8.11 | ||

34 | Apr 17 | Shannon-Nyquist theorem, Isoperimetric inequality | HW9 solutions written by our grader | ||

35 | Apr 20 | The Laplace Transform | 8.8, 8.9 | HW11 posted | Due April 27 |

36 | Apr 22 | Inversion by convolution, the Bromwich Integral | 8.9, 14.7 lecture notes | ||

37 | Apr 24 | Green's functions | 8.11, 8.12 | HW12 posted | |

38 | Apr 27 | Green's functions, weak solutions | 8.11, 8.12 | ||

39 | Apr 29 | Finish Green's functions | lecture notes | HW10 solutions posted HW11 solutions posted | |

40 | May 1 | Review, evaluations | HW12 solutions written by our grader |

**Course Outline:**

- Infinite Series (Chapter 1)
- Linear Algebra (Chapter 3)
- Partial Differentiation (Chapter 4)
- Complex Analysis (Chapters 2 & 14)
- Fourier Series & Transforms (Chapter 7)
- Laplace Transforms (Chapter 8, end)
- Calculus of Variations (Chapter 9)

*Midterm 1, Wednesday 2/18*

*Midterm 2, Friday 3/20 *

*Final Exam, Monday 5/11*