• 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