Week	Lecture Topics	Reading	Tutorial Problems	Practical Exercise
Week 1	Parameterisation of curves; time as a variable	Ch. 14	No tutorial	No practical
	2-d and 3-d curves and surface intersection	Ch. 13.5
	Curves as vectors: motion; velocity; acceleration
Week 2	Motion in a circle; arc length; line integrals	Ch. 14	Ch. 13.5- 2	Basic matlab: plotting
	Rules for vector calculus: derivatives; integrals Line integrals and applications: magnetic fields	Ch. 17.2	Ch. 14.2- 24 Ch. 14.4- 14, 35	a function
Week 3	Functions of several variables: examples	Ch. 15.1	Ch. 14.3- 2	More matlab basics:
	Cartesian coordinates: distance; graphs and surfaces Surfaces and examples; contour diagrams	Ch. 13.6	Ch. 14.4- 16 Ch. 17.2- 10, 22
Week 4	Contour diagrams and linear functions	Ch. 15.2	Ch. 15.1- 30, 38	Plotting surfaces and
	Functions of 3 variables and level surfaces	Ch. 13.6	Ch. 13.6- 36, 48	contours
	Continuity
Week 5	Partial derivatives and surfaces	Ch. 15.3	Ch. 15.1- 56, 59	Surfaces and
	Computing and interpreting partial derivatives	Ch. 15.4	Ch. 15.2- 8, 14	continuity
	Differentiability and tangent plane
Week 6	Gradients and directional derivatives   Chain rule; 2nd order partial derivatives; Conservative fields	Ch. 15.5   Ch. 15.6 Ch. 17.3	Ch. 15.3- 46, 69   Ch. 15.4- 2, 36	Local maxima and   minima
Week 7	Second order Taylor Series, local extrema		No tutorial	No practical
	Classification of local extrema	Ch. 15.7
	Review for mid-semester exam ( Wednesday- Anzac Day holiday )
Week 8	Global extrema	Ch. 15.7	Mid-semester	Work on Project 1
	Lagrange multipliers examples	Ch. 15.8	exam
Week 9	simple diff. equations: motion of projectiles	Ch. 14.4	Ch. 15.5- 10
	differential equations: definitions and slope fields	Ch. 10.1	Ch. 15.6- 16, 53	Project 1 due
	( Monday- Labour Day holiday )		Ch. 17.3- 10
Week 10	numerical example: Euler's method separable equations: first order linear and nonlinear Solution by integrating factor	Ch. 10	Ch. 15.7- 4, 34 Ch. 15.8- 4, 24	Numerical approx.  of surfaces by  Taylor series
Week 11	first order equations and applications	Ch. 18	Ch. 14.4- 25	Euler's method for
	second-order differential equations: constant coeff.		Ch. 10.3- 2, 10	ODE's
	simple harmonic motion		Ch. 10.4- 14
Week 12	examples: damped oscillations		Ch. 10.6- 18	Work on Project 2
	particular solutions to second-order equations		Ch. 18.1- 22
	examples of forced oscillations	Ch. 18	Ch. 18.2- 9, 10
Week 13	systems of first-order differential equations		TBA	Project 2 due
	review and examples