Calculus IMAT 131Spring 2009 

Mathematics department  
Julia Viro 
Instructors  Schedule  Assignments  Exams  Generalities  Help 

Week of  Contents  Sections 

1/261/30  Functions and their graphs. Domain, range. Even and odd functions, increasing and decreasing functions. Operations on functions: sum, difference, product, quotient, composition. Elementary vs nonelementary functions.  1.2, 1.3 
2/22/6  Basic elementary functions: linear functions, polynomials, rational, power, trigonometric and exponential functions. Inverse functions. Logarithm. Inverse trigonometric functions: arcsine, arccosine, arctangent.  1.2, 1.5, 1.6 
2/92/13  The limit of a function. Limit laws. Continuity. Types of discontinuity. Squeeze theorem. Intermediate value theorem. Limits involving infinity. Vertical, horizontal and oblique asymptotes. Calculating technique for limits.  2.12.5 
2/162/20  The derivative of a function and its geometrical meaning. Tangent line. Derivative as velocity. Linearization. Derivatives of higher orders. Derivatives and shapes of curves.  2.62.8, 3.8, 4.24.3 
2/232/27  Review for Midterm I. Midterm I is on Wednesday 2/25 at 8:3010:00pm  
3/23/6  Differentiation laws. Chain rule. Derivative of inverse function. Derivatives of elementary functions. Differentiation technique.  3.13.5 
3/93/13  Implicit differentiation. Parametric curves. Related rates problems.  3.63.7, 1.7, 4.1 
3/163/20  Review for Midterm II. Midterm II is on Monday 3/23 at 8:3010:00pm  
3/233/27  Rolle's, Lagrange's and Cauchy's theorems. Indefinite forms and L'Hopital's rule.  4.3, 4.5 
3/304/3  Graphing.  4.2, 4.4 
4/64/10  Spring recess  
4/134/17  Extreme Value Theorem. Optimization problems. Antiderivative and indefinite integral.  4.2, 4.6, 4.9 
4/204/24  Definite integral and its properties. Definite integral as limit of Riemann sums.  5.15.2 
4/275/1  The Fundamental Theorem of Calculus. Integration by substitution.  5.35.5 
5/45/8  Review for Final.  
Friday 5/15 8:0010:30am 
Final exam 