## MA1132 -- Hilary 2017

### Calendar:

Lecture Topics covered
1 (16.01) Parametric equations and vector-valued functions (Section 12.1)
2 (18.01) Calculus of vector-valued functions and arc length (Sections 12.2-12.3)
3 (23.01) TNB Frames and curvature (Sections 12.4-12.5)
4 (25.01) Motion, velocity, acceleration, and physics (Section 12.6)
5 (30.01) Multivariable functions, limits, and continuity (Sections 13.1-13.2)
6 (01.02) Partial derivatives (Section 13.3)
7 (06.02) Tangent planes and linear approximation (Section 13.4)
8 (08.02) The Chain Rule (Section 13.5)
9 (13.02) Directional derivatives and gradients (Section 13.6)
10 (15.02) Tangent planes and normal vectors (Section 13.7)
11 (20.02) Maxima and Minima (Section 13.8)
12 (22.02) Lagrange Multipliers (Section 13.9)
13 (06.03) Double integrals and the volume problem (Section 14.1)
14 (08.03) Double integrals over more general regions (Section 14.2)
15 (13.03) Double integrals in polar coordinates (Section 14.3)
16 (15.03) Surface area (Section 14.4)
17 (20.03) Triple integrals (Section 14.5)
18 (22.03) Triple integrals in cylindrical and spherical coordinates (Section 14.6)
19 (27.03) Changes of variables in multiple integrals (Section 14.7)
20 (29.03) Preview of what comes after this class
Final week Review days

### Sample/Old Exams

Sample Exam

Sample Exam Solutions

Previous exams, and some previous solutions, can also be found on Professor Frolov's advanced calculus website.

### Homework

Homework 1

Homework 1 Solutions

Homework 2

Homework 2 Solutions

Homework 3

Homework 3 Solutions

Homework 4

Homework 4 Solutions

Homework 5

Homework 5 Solutions

Homework 6

Homework 6 Solutions

Homework 7

Homework 7 Solutions

Homework 8

Homework 8 Solutions

Homework 9

Homework 9 Solutions

Homework 10

Homework 10 Solutions

### Tutorials

Tutorial 1

Tutorial 1 Solutions

Tutorial 2

Tutorial 2 Solutions

Tutorial 3

Tutorial 3 Solutions

Tutorial 4

Tutorial 4 Solutions

Tutorial 5

Tutorial 5 Solutions

Tutorial 6

Tutorial 6 Solutions

Tutorial 7 Solutions

Tutorial 8 Solutions

Tutorial 9

Tutorial 9 Solutions