Course Objectives:

1.         Differentiation of algebraic, trigonometric, exponential, and logarithmic functions.
2.         Integration of Algebraic, trigonometric, exponential, and logarithmic functions.
3.         Solve applied problems using Differential and Integral Calculus concepts.
 

Topical Outline:

1.         Determine if the limit of a function exists by using algebraic or graphing techniques.
2.         Identify vertical and horizontal asymptotes of a function by using algebraic techniques or limit theory.
3.         Differentiate algebraic functions using the power rule, product rule, and quotient rule.
4.         Differentiate trigonometric functions.
5.         Differentiate algebraic and trigonometric composite functions using The Chain Rule alone and in combination with power rule, product rule, and quotient rule.
6.         Perform implicit differentiation for functions not explicitly stated in terms of a single variable.
7.         Differentiate logarithmic functions and composite logarithmic functions.
8.         Differentiate exponential functions and composite exponential functions.
9.         Differentiate inverse trigonometric functions and composite inverse trigonometric functions.
10.       Perform successive differentiation to find higher order derivatives.
11.       Solve rectilinear motion problems by using the first derivative as instantaneous velocity and the second derivative as acceleration.
12.       Solve problems in which an unknown quantity is changing by equating it to related rates of quantities whose rates of change are known.
13.       Find intervals of increase/decrease and the stationary points of a function by using the First Derivative Test
14.       Determine the equation of the tangent line to a function at any given point.
15.       Find intervals of upward/downward concavity and the location of inflection points by using the Second Derivative Test.
16.       Solve optimization problems with the help of maximum-minimum theory.
17.       Differentiate complex functions by using logarithmic differentiation.
18.       Approximate non-linear functions and calculate the error such a procedure generates by using differentials and the derivative of the function.
19.       Determine the limit of a function by adequately applying L’Hopital’s rule.
20.       Calculate the anti-derivative for basic functions
21.       Integrate composite functions by the technique called Asubstitution@.
22.       Integrate trigonometric and inverse trigonometric functions.
23.       Evaluate definite integrals by using the Fundamental Theorem of Calculus.
24.       Calculate the average value of a function including average velocity.
25.       Evaluate definite integrals by the ASubstitution@ method.