Section Course Goals and Objectives

Objectives: Course Goals

Students gain an understanding of the fundamentals of differential and integral calculus and its applications in the physical and social sciences.
Students solifify their abilities in the use of algebra, trigonometry, and calculus.
Students develop an appreciation for the foundations of the real number system
Students increase their problem solving abilities.
Students increase their mathematical maturity and confidence in working through mathematical challenges.

The course is based around the following Course Learning Objectives.

Find limits graphically, numerically, and analytically. (LT1, LT2, LT3)
Determine where a function is and is not continuous. (LT4)
Determine limits with infinite inputs and infinite outputs. (LT5, LT6)
Find derivatives using the limit definition of the derivative. (DF2)
Compute basic derivatives using algebraic rules. (DF3)
Compute derivatives using Product, Quotient, and Chain Rules. (DF4, DF5, DF6)
Compute derivatives of implicitly-defined functions. (DF7)
Compute derivatives of inverse trig functions and log functions. (DF8)
Use the derivative to find tangent lines, and use the tangent line for linear approximation. (AD1, AD2)
Model and analyze scenarios using related rates. (AD3)
Use the Extreme Value Theorem to find global max and min values. (AD4)
Use derivatives to determine where a function is increasing, decreasing, concave up, concave down, and to find local extrema and inflection points. (AD5, AD6, AD7)
Apply optimization techniques to solve various problems. (AD8)
Approximate definite integrals using Riemann sums. (IN2)
Determine basic antiderivatives. (IN3)
Evaluate a definite integral using the Fundamental Theorem of Calculus. (IN5)
Use definite integrals to find the area under a curve and the area between curves. (IN7, IN8)
Evaluate various integrals using the substitution method. (TI1)