# Math 241 Section D1: Calculus III, Summer 2013

**Instructor:** Hong
Liu

**Office:** 224 Illini Hall

**Email:** hliu36-at-
illinois.edu

**Time and place:** MTWTF 11:00am- 12:20pm, 1064 Lincoln
Hall

**Office Hour:** MWF 12:20pm- 1:00pm,

**Mid-terms:** On the Friday of 2nd, 4th and 6th week

**Final exam:** 1064 Lincoln Hall, 1-3pm on Saturday, August 3, 2013

### Homeworks are online: WebAssign

## Schedule

### Week 1

**June 10** Introduction (§12.1).
**HW 1**, due Thursday, June 13.

**June 11** Vectors (§12.2) and dot
product (§12.3). Lecture
note 1 and 2.

**June 12** projections (§12.3) and equation for lines (§12.5). **HW 2**, due Friday, June 14.

**June 13** equation for lines and planes (§12.5). Lecture
note 3 and 4. **HW 3**, due Monday, June 17.

**June 14** cross product (§12.4). **HW 4**, due Wednesday, June 19.

### Week 2

**June 17** cross product, triple product (§12.4). Lecture
note 5 and 6. **HW 5**, due Thursday, June 20.

**June 18** functions with several variables (§14.1). Lecture
note 7.

**June 19** quadric surfaces (§12.6). Lecture
note 8.
The following sources could be helpful for graphing.

I: Guide to quadric surface. II: 3D graphing tool. III: Wolfram alpha.

**June 20** Review for midterm 1. Here are previous midterms for practice.

2012 midterm 1 , Solutions; 2011 midterm 1 , Solutions; 2010 midterm 1 , Solutions

**June 21** **Midterm 1.** Solutions; In class! It covers Chapter 12 and §14.1

### Week 3

**June 24** Limits and continuity (§14.2). Lecture
note 9. **HW 6**, due Wednesday, June 26. **HW 7**, due Thursday, June 27.

**June 25** Partial derivatives (§14.3). Lecture
note 10. **HW 8**, due Friday, June 28. **HW 9**, due Sunday, June 30.

**June 26** Tangent planes and linear approximation (§14.4). Lecture
note 11.

**June 27** Chain rule (§14.5). Lecture
note 12. **HW 10**, due Sunday, June 30.

**June 28** Chain rule and implicit differentiation (§14.5). Lecture
note 13. **HW 11**, due Monday, July 1.

### Week 4

**July 1** Directional derivatives and gradient vectors (§14.6). Lecture
note 14. **HW 12**, due Tuesday, July 2.

**July 2** Review for midterm 2.

**July 3**
**Midterm 2.**
Solutions;
In class! It covers §14.1 to §14.6

### July 4th Break

### Week 5

**July 8** Local min/max via 2nd derivative test (§14.7). Lecture
note 15. **HW 13**, due Tuesday, July 9.

**July 9** Absolute min/max (§14.7); Lagrange multipliers (§14.8). Lecture
note 16. **HW 14**, due Wednesday, July 10.

**July 10** Vector functions, curves in space, length and curvature of a curve (Chapter 13). Lecture
note 17. **HW 15**, due Thursday, July 11.

**July 11** Vector fields (§16.1); Integration along curves (§16.2). Lecture
note 18. **HW 16**, due Saturday, July 13.

**July 12** Integrating Vector fields (§16.2); fundamental theorem of line integral (§16.3). Lecture
note 19. **HW 17**, due Sunday, July 14.

### Week 6

**July 15** Conservative vector fields (§16.3). Lecture
note 20. **HW 18**, due Wednesday, July 17.

**July 16** Multivariable integral (§15.1,§15.2). Lecture
note 21. **HW 19**, due Thursday, July 18.

**July 17** Integrating over more complicated regions; polar coordinates (§15.3,§15.4). Lecture
note 22. **HW 20**, due Sunday, July 21.

**July 18** Review for midterm 3.

**July 19**
**Midterm 3.**
Solutions;
In class! It covers §13.1-3 §14.7-8; §16.1-3; §15.1-4.

### Week 7

**July 22** Triple integral (§15.6). Lecture
note 23. **HW 21**, due Wednesday, July 24.

**July 23** Cylindrical/Spherical coordinates (§15.7,8). Lecture
note 24. **HW 22**, due Thursday, July 25.

**July 24** Green's Theorem (§16.4); Curves in space and tangent plane (§16.6). Lecture
note 25. **HW 23**, due Friday, July 26.

**July 25** Surface integral (§16.7). Lecture
note 26. **HW 24**, due Saturday, July 27.

**July 26** Flux and Divergence theorem in R^2 (§16.5/7). Lecture
note 27.

### Week 8

**July 29** Flux and Divergence theorem in R^3 (§16.7/9) Curl of a vector field (§16.5). Lecture
note 28. **HW 25**, due Wednesday, July 31.

**July 30** Stokes Theorem (§16.8). Lecture
note 29. **HW 26**, due Thursday, Aug 1.

**July 31** Conservative vector fields in R^3 (§16.5). Lecture
note 30. **HW 27**, due Thursday, Aug 1.

**Aug 1** Review for final.
Practice final
Solutions;

**Aug 2** Reading day.

**Aug 3** **FINAL BOSS!** 1064 Lincoln Hall, 1-3pm