ENGR 233 winter 2021

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Textbook:

Advanced Engineering Mathematics, by Dennis G. Zill and Warren S. Wright, 6th Edition1, Published by Jones and Bartlett.

Grading Scheme:

1. Assignments (WeBWorK) 10%
2. Team projects (2) 10% (5% each, 1 hour; during tutorials in teams of 2 or take home; online)
3. Term tests (2) 40%, (20% each, during lectures or tutorials in COLE)
4. Final exam 40% (2 to 3 hours in COLE)

Course Description:

This course introduces first year engineering students to multivariable calculus and its applications to mathematical models.
The main topics include: Vector functions; Functions of several variables; Differential vector calculus; Integral
calculus for vectors; Double and triple integrals; Line and surface integrals; Stokes’ Theorem; Divergence Theorem;
Applications in applied science and engineering.

ENGR 233 winter 2021

Week 1 Jan 11:

Review of the following topics:

• 7.1 Vectors in 2-space; problems: 1,21,30,41,50
• 7.2 Vectors in 3-space; 11,24,32,34,52
• 7.3 Dot product: 12,15,23,29,31, 41,48
• 7.4 Cross product: 3,13,22,28,41,42,45,49,52

Lecture 1. Vectors in the plane and in the space

Lecture 1 (cont.) Dot product

Lecture 2. Signed area

Lecture 3. Cross-product

Tutorial 1:

Week 2 Jan 18:

• 7.5 Lines and planes in space: 5,12,17,24,33,36,39,49,57,61,66,75
• 9.1 Vector functions: 1,4,10,18,25,34,3639,42,45

Lecture 4. Lines and planes

Lecture 5 Vector functions

Lecture 6 Some dynamical problems

Tutorial 2:

Week 3 Jan 25:

• 9.2 Motion on a curve: 4,9,11,13,14,19,22,27,28,29
• 9.3 Curvature. Components of Acceleration: 1,6,9,16,17,20,23

Lecture 7 Curvature:

Lecture 7.2 Acceleration decomposition

Lecture 7.3 Osculating circle

Tutorial 3

Week 4 Feb 1:

• 9.4 Partial derivatives: 2,3,6,9,15,21,24,26,27,36,39,42,48,49,51,55,56,57
• 9.5 Directional derivative: 3,6,12,14,15,18,24,27,28,33,41,4344

Lecture 8 Partial derivatives

Lecture 9 Gradient and Directional derivatives

Tutorial 4:

Week 5 Feb 8:

• 9.6 Tangent planes and normal lines: 3,4,14,15,25,34,39
• 9.7 Curl and Divergence: 7,11,15,21,24,27,30,39,40,43,44

Lecture 10 Tangent lines and planes

Lecture 11 Higher order partial derivatives

Lecture 12 Vector fields Divergence

Lecture 13 Curl of a velocity field

Tutorial 5

Week 6 Feb 15:

• 9.8 Line integrals 3,6,9,15,21,25,27,28,30,33,36,40
• 9.9 Independence of path 3,6,15,18,21,24,26,27,28,30

Lecture 14 Line integral

Lecture 14 cont Line integral aling closed curves

Lecture 15 Path independence of line integrals

Lecture 16 Irrotational and potential vector fields

Tutorial 6

Week 7:

• Term Test 1 (1-hour exam during ) on material Chap 7 + Sections 9.1 through 9.7

Week 7 Feb 22:

• 9.10 Double integrals: 3,5,9,15,18,21,24,27,33,36,39,42,45,52,62,65,68

Lecture 17 Double integral

Lecture 18 Volume of simple bodies

Lecture 19 Lamina

Tutorial 7

Week 8 Mar 8:

• 9.11 Double integral in polar coordinates: 3,6,11,12,19,24,27,29,30,33,34
• 9.12 Green’s theorem: 3,4,6,8,12,18,19,23,24,25,27,33

Lecture 20 Double integral in polar coordinates

Lecture 21 Green’s Theorem

Lecture 22 Applications of the Green’s Theorem

Tutorial 8

Week 9 Mar 15:

• 9.13 Surface Integrals: 2,4,6,8,10,11,15,17,18,24,28, 29,32,33,36,37,39

Lecture 23 Surface area

Lecture 24 Surface integral

Lecture 25 Flux of a vector field through a surface

Week 10:

• Term Test 2 (1-hour exam during ) on material of Section 9.8 through Section 9.13

Week 10 Mar 22:

• 9.14 Stokes theorem: 3,4,6,9,10,12,13,14,18

Lecture 26 Stokes Formula

Lecture 27 Stokes Formula cont

Tutorial 9

Week 11 Mar 293:

• 9.15 Triple Integrals: 3,6,9,13,14,15,21,23,24,27,32,34,45,48,

Lecture 28 Triple Integral

Lecture 29 Triple integral in cylindrical coordinates

Lecture 30 Triple integral, some examples

Lecture 31 Triple integral in spherical coordinates

Week 12 Apr 5,4:

• 9.15 Triple Integrals: 51,54,57,68,69,72,75,76,78,81
• 9.16 Divergence theorem: 2,3,6,9,11,12,13,15,17,21,22

Lecture 32 The Divergence Theorem

Lecture 33 Some applications of the Divergence Theorem

Lecture 34 Applications of the Divergence Theorem 2

Week 13 Apr 12:

• 9.17 Change of variables in multiple integral: 3,5,7,8,9,10,13,15,17,22,23,25,27

Lecture 35 Change of variables in double integral

Time permitted:

• Review: 1-20,24,26,29,30,32,36,38,43,46,50,51,53,54,56,57,58,60,63,65