Calculus. reparation for Calculus, Limits and Their Properties, and Differentiation. Gorman Learning Center (052344) Basic Course Information

Transcription

1 Calculus Gorman Learning Center (052344) Basic Course Information Title: Calculus Transcript abbreviations: calcag / calc Length of course: Full Year Subject area: Mathematics ("c") / Calculus UC honors designation? No Prerequisites: None Co-requisites: None Integrated (Academics / CTE)? No Grade levels: 11th, 12th Course learning environment: Classroom Based Course Description Course overview: Calculus is an in-depth study of functions, graphs, limits, derivatives, definite integrals, antiderivatives, differential equations and real-world applications of differentiation and antidifferentiation. Concepts will be explored graphically, numerically, algebraically, and verbally. Subtopics include products, quotients, the calculus of logarithmic functions, growth and decay, plane and solid figures, algebraic calculus of motion. Technology tools such as graphing calculators and other graphing applications will be used regularly in this course. Course content: Calculus reparation for Calculus, Limits and Their Properties, and Differentiation

2 Graphs and Models Linear Models and Rates of Change Functions and Their Graphs Fitting Models to Data A Preview of Calculus Finding Limits Graphically and Numerically Evaluating Limits Analytically Continuity and One-Sided Limits Infinite Limits The Derivative and the Tangent Line Problem Basic Differentiation Rules and Rates of Change Product and Quotient Rules and Higher-Order Derivatives The Chain Rule Implicit Differentiation Related Rates Applications of Differentiation Extrema on an Interval Rolle's Theorem and the Mean Value Theorem Increasing and Decreasing Functions and the First Derivative Test Concavity and the Second Derivative Test Limits at Infinity A Summary of Curve Sketching Optimization Problems Newton's Method

3 Differentials Integration and Logarithmic, Exponential, and Other Transcendental Functions Antiderivatives and Indefinite Integration Area The Fundamental Theorem of Calculus Integration by Substitution Numerical Integration The Natural Logarithmic Function: Differentiation The Natural Logarithmic Function: Integration Inverse Functions Exponential Functions: Differentiation and Integration Bases Other Than e and Applications Inverse Trigonometric Functions: Differentiation Inverse Trigonometric Functions: Integration Hyperbolic Functions

4 Differential Equations and Applications of Integration Slope Fields and Euler's Method Differential Equations: Growth and Decay Separation of Variables and the Logistic Equation First-Order Linear Differential Equations Area of a Region Between Two Curves Volume: The Disk Method Volume: The Shell Method Arc Length and Surfaces of Revolution Work Moments, Centers of Mass, and Centroids Fluid Pressure and Fluid Force Integration Techniques, L'Hopital's Rule, and Improper Integrals

5 Basic Integration Rules Integration by Parts Trigonometric Integrals Trigonometric Substitution Partial Fractions Integration by Tables and Other Integration Techniques Indeterminate Forms and L'Hopital's Rule Improper Integrals Infinite Series Sequences Series and Convergence The Integral Test and p-series Comparisons of Series Alternating Series The Ratio and Root Tests Taylor Polynomials and Approximations Power Series Representation of Functions by Power Series Taylor and Maclaurin Series

6 Conics, Parametric Equations and Polar Coordinates, and Vectors and the Geometry of Space Conics and Calculus Plane Curves and Parametric Equations Parametric Equations and Calculus Polar Coordinates and Polar Graphs Area and Arc Length in Polar Coordinates Polar Equations of Conics and Kepler's Laws Vectors in the Plane Space Coordinates and Vectors in Space The Dot Product of Two Vectors The Cross Product of Two Vectors in Space Lines and Planes in Space Surfaces in Space Cylindrical and Spherical Coordinates

7 Vector-Valued Functions and Functions of Several Variables Vector-Valued Functions Differentiation and Integration of Vector-Valued Functions Velocity and Acceleration Tangent Vectors and Normal Vectors Arc Length and Curvature Introduction to Functions of Several Variables Limits and Continuity Partial Derivatives Differentials Chain Rules for Functions of Several Variables Directional Derivatives and Gradients Tangent Planes and Normal Lines Extrema of Functions of Two Variables Applications of Extrema of Functions of Two Variables Lagrange Multipliers Multiple Integration

8 Iterated Integrals and Area in the Plane Double Integrals and Volume Change of Variables: Polar Coordinates Center of Mass and Moments of Inertia Surface Area Triple Integrals and Applications Triple Integrals in Cylindrical and Spherical Coordinates Change of Variables: Jacobians Vector Analysis Vector Fields Line Integrals Conservative Vector Fields and Independence of Path Green's Theorem Parametric Surfaces Surface Integrals Divergence Theorem Stoke's Theorem

9 Course Materials Textbooks Title Author Publisher Edition Website Primary Calculus Ron Larson, Robert P. Hostetler and Bruce H. Edwards Houghton Mifflin Eighth edition/2006 [ empty ] Yes