MATH 1081 - Single Variable Calculus I

1. Antidifferentiation, the indefinite integral
2. Application of the Definite Integral
   1. Area
3. Applications of the Derivative
   1. Elementary differential equations and their solutions
   2. Optimization
   3. Taylor polynomials
   4. Related rates
   5. Approximations
   6. Newton’s Method
4. Continuity
   1. Intuitive understanding
   2. Definition of continuity at a point
   3. Continuity on an interval and discontinuities
5. Limits
   1. Intuitive understanding
   2. Limit theorems
6. Preliminary concepts
7. The Definite Integral
   1. Intuitive understanding
   2. Approximating sums
   3. The Fundamental Theorem of calculus
8. The Derivative
   1. Intuitive or geometric interpretation
   2. Definition of the derivative
   3. Differentiation formulas
   4. Composite functions-chain rule
   5. Higher order derivatives
   6. Implicit differentiation

1. Find the area under a curve by using the Fundamental Theorem of Calculus.
2. Model and solve optimization problems by applying and analyzing the derivative.
3. Approximate the area under a curve with approximating sums by hand and with technology.
4. Analyze the geometry of a function by using differentiation.
5. Determine the derivative of a function graphically, numerically, and symbolically.
6. Demonstrate critical and logical reasoning when solving problems.
7. Find the anti-derivative of polynomials.
8. Explain the relationships between a function, its derivative, and its second derivative.
9. Communicate clearly a problems solution and its explanation for the intended audience in terms of the problem posed.

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