Please note: This is not a course syllabus. A course syllabus is unique to a particular section of a course by instructor. This curriculum guide provides general information about a course.
This is the first course in the calculus sequence. It covers algebraic and transcendental functions, rate of change, limits, continuity, differentiation of algebraic, trig, exponential, logarithmic and hyperbolic functions, differentials, applications of differentiation, definite and indefinite integrals, area between curves, volumes and other applications of integration, indeterminate forms and L’Hopital’s Rule.
Represent functions verbally, numerically, graphically, algebraically
Graph, evaluate and use common functions (linear, polynomial, power, rational, trigonometric, algebraic, exponential, logarithmic)
Perform operations on functions (transformations, algebraic combinations, composition)
Use graphing calculators to graph functions
Exponential functions (evaluate, graph, applications)
Inverse functions (inverses in general and inverse trig functions)
Logarithms (properties, natural logs, solve equations, evaluate)
Trigonometric functions (properties, graphs, identities)
Tangent and velocity problems
Limit of a function
Calculate limits using the Limit Laws, also one-sided limits
The precise (? and ?) definition of a limit
Continuity
Limits at Infinity : Horizontal Asymptotes
Tangents, Velocities, and Other Rates of Change
Derivatives (definition as a limit, interpretation as the slope of a tangent, interpretation as a rate of change, derivation as a function, when differentiation fails)
Derivatives of polynomials and exponential functions
Product Rule for differentiation
Quotient Rule for differentiation
Applications of rates of change in natural and social sciences
Derivatives of trig functions
The Chain Rule
Implicit Differentiation.
Higher derivatives
Derivatives of logarithmic functions
Logarithmic differentiation
Hyperbolic functions (definitions, identities, derivatives)
Related Rates
Linear approximations and differentials
Maximum and Minimum values
Mean Value Theorem
How derivatives (f ’ and f ’’ ) relate to the shape of a graph
Indeterminate forms and L’Hospital’s Rule
Curve sketching using intercepts, domain, symmetry, asymptotes, f ’, f ’’, etc.
Graphing with calculus and calculators
Optimization problems
Applications of the derivative to business and economics
Newton’s Method
Antiderivatives
Area under a curve and distance
Definite integrals
The Fundamental Theorem of Calculus
Indefinite integrals
Integration by substitution
The natural logarithm defined as an integral
Areas between curves
Volumes of solids of revolution using disks, washers, shells
Volumes of solids with known cross-sections
Work
Average value of a function