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Learning Outcomes for 3450:221 Analytic Geometry and Calculus I
Students are expected to be able to
- Communicate mathematical results through the proper use of mathematical notation and words
- Learn the definition of the limit of a function, how to calculate limits using the limit laws, and the definition of continuity
- Learn the definition of the derivative of a function and how to differentiate polynomial, exponential, trigonometric, and logarithmic functions, as well as products, quotients and compositions of these functions.
- Learn applications of the derivative
- Learn the definitions of the definite and indefinite integral, the Fundamental Theorem of Calculus, and the substitution rule
- Topical Outline
- Exponential Functions
- Inverse Functions and Logarithms
- The Tangent and Velocity Problem
- The Limit of a Function
- Calculating Limits using the Limit Laws
- The Precise Definition of a Limit
- Continuity
- Limits at Infinity: Horizontal Asymptotes
- Derivatives and Rates of Change
- The Derivative as a Function
- Derivatives of Polynomials and Exponential Functions
- The Product and Quotient Rules
- Derivatives of Trigonometric Functions
- The Chain Rule
- Implicit Differentiation
- Derivatives of Logarithmic Functions
- Exponential Growth and Decay
- Related Rates
- Linear Approximations and Differentials
- Hyperbolic Functions
- Maximum and Minimum Values
- The Mean Value Theorem
- How Derivatives Affect the Shape of a Graph
- Indeterminate Forms and l’Hopital’s Rule
- Summary of Curve Sketching
- Optimization Problems
- Newton’s Method
- Antiderivatives
- Areas and Distances
- The Definite Integral
- Definite Integral
- The Fundamental Theorem of Calculus
- Indefinite Integrals and the Net Change Theorem
- The Substitution Rule