MATA32: Calculus for Management I (Winter '10)



Instructor: Leo Goldmakher

Teaching Assistants:

(due 1 week from date posted)
Jan. 5 motivating integration (average speed example);
intuition for derivative (zoom in!);
Andy likes my shirt.
      Course syllabus
Jan. 7 Sets (e.g. natural numbers, integers, rationals, reals,
undergraduates at UTSc, etc.)
The square root of 2 is not rational.
Functions -- definition, examples, non-examples.
Assignment 1      
Jan. 12 Functions: domain, range, examples        
Jan. 14 Inverse functions, exponential functions Assignment 2 Quiz 1 Solution 1  
Jan. 19 Logarithmic functions; compounded interest        
Jan. 21 General formula for compounded interest;
Menagerie of functions and order of growth;
The number e and the natural logarithm;
Frequently compounded interest and e;
Exponential decay and half-life.
Assignment 3 Quiz 2 Solution 2  
Jan. 26 Set the midterm date for March 4th (in class);
Practiced manipulating exponentials and logs;
Discussed APR, nominal rates, effective rates,
future value, and present value;
Started a problem on carbon dating and half-life.
Jan. 28 Redid half-life example (carbon dating);
Example of future value: borrowing from parents;
Continuously compounded interest;
Equations of Value: two arguments, same conclusion;
Geometric series.
Assignment 4 Quiz 3 Solution 3 Puzzler
Feb. 2 More on equations of value;
Sequences vs series; geometric series;
Sigma notation.
Feb. 4 More on series, sigma notation, geometric series (Zeno's paradox);
RRSP and annuities: amount (future value) and present value.
Assignment 5 Quiz 4 Solution 4  
Feb. 9 Reviewed how to calculate PV and FV of an annuity;
Loan amortization.
Feb. 11 Continuity (on an interval, at a point);
Types of discontinuities:
    end of domain, bulletholes, jump discontinuities, vertical asymptotes;
Horizontal asymptotes and limits;
Examples of determining limits pictorially and algebraically.
Assignment 6 Quiz 5 Solution 5 Midterm Practice Problems
Feb. 23 Overview of finding limits;
Problem on making a piecewise function continuous.
Feb. 25 Making a piecewise function continuous;
Geometric definition of derivative;
Limit definition of derivative;
Examples of exactly evaluating a derivative;
Examples of approximating a derivative.
Read sections 11.1 and 11.2
through page 492, and
study for midterm!
Quiz 6 Solution 6  
Mar. 2 The derivative function;
Sketch f '(x) given the graph of f(x);
Basic properties of derivatives.
Mar. 4 Midterm exam Assignment 7   Midterm Solutions  
Mar. 9 Derivative of x^n, ln(x), e^x; product rule.        
Mar. 11 More differentiation, including chain rule, quotient rule, a^x, x^x, etc. Assignment 8      
Mar. 16 GUEST LECTURE: 11.3        
Mar. 18 GUEST LECTURE: 11.4--11.5 Assignment 9 Quiz 7 Solution 7  
Mar. 23 Differentiating logarithms to any base;
Implicit differentiation.
Mar. 25 Implicit differentiation problem (find equation of tangent line!);
The second derivative and acceleration;
Optimization: finding absolute / relative maxima and minima;
Applications of optimization to economics, and gardening.
Assignment 10 Quiz 8 Solution 8  
Mar. 30 The second derivative test;
Distance traveled is area under the speed function.
Apr. 1 The definition of the integral (area, but possibly negative);
Finding the average of a continuous function (e.g. weather, speed);
Integration using geometry;
The fundamental theorem of calculus;
  Quiz 9 Solution 9