Preparation for the final exam of Math 102 (2009)

   (Formulas for some basic trig idendentities will be prodived. No calculator is allowed.)
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   I.   Problems covered: HW#1-HW#13 all the assigned problems.

   II.  Important materials for your study: 

	1. Math Club study guides: Math 102 and Math 100/180.
	2. Previous final exam(s) posted the Math102 websites and at
        http://www.math.ubc.ca/~yxli/m102_01_final.pdf
        (Do not expect to get the same type of problems in this year!!!)
	3. Lecture notes, online notes, reference book(s)

   III. Materials covered:
     (All listed will be tested. Those with an asterisk carry a heavier weight!)

	1. Functions
	   (1) Definition of a function and its inverse
	   (2)* Composite functions (how to recognize them under different situations)	
	   (3) Elementary functions and properties: power, polynomial, exp, log, trig
	   (4) Relation between the graph of f(x) and that of a shifted form of f(x)
	   (5) Odd and even functions

	2.* Derivatives
	   (1) Definition and evaluation of some simple limits
	   (2) Secant lines and tangent lines
	   (3) Average rate of change and instantaneous rate of change
	   (4) Displacement-velocity-acceleration
	   (5) Rules for differentiation: product, quotient, and chain rules
	   (6) Implicit differentiation

	3.* Applications
	   (1) Graph sketch:
		(i)  Analytic: 		f(x)  ==> graph
		(ii) Visual estimate: 	graph of f(x) <==> graph of f'(x) 
	   (2) Optimization
	   (3) Related rates
	   (4) Simple models using differential equations
		(i)   Newton's law of cooling
                (ii)  Terminal speed
                (iii) Infusion/mixing models
		(iv)  Population models

	4. Differential equations
	   (1) Basic concepts
		(i)   Order and arbitrary constants in the general solution
		(ii)*  Check if a function is a solution of a DE (How to?)
		(iii) Initial conditions (How to find them? How many?)
		(iv)  IVP: initial value problems
	   (2)* Simple exponential growth/decay
	   (3)  Harmonic oscillations
	   (4)* Exponential approach to a nonzero steady state
	   (5)* Qualitative method:
		(i)   Steady state (Definition and how to find?)
		(ii)  Slope filed and the direction of solution flow
		(iii) Stability of a steady state
		(iv)  Long time behaviour and steady state(s)

        5.* Approximation methods
           (1) Linear (tangent line) approximation
           (2) Newton's method for finding zeros(roots), 
		intersection points, critical points, etc.