# Calculus I/II

COURSE SYLLABUS FOR CALCULUS I/II

CVCC Course Number - MATH 263/264 - 8 credit hours

INSTRUCTOR: Mr Howard       ROOM: 106

COURSE DESCRIPTION: A college level study of:
(Calculus I) differential calculus, this course includes the study of limits, continuity, derivatives (concept and definition), derivatives of parametric equations and polar curves, differentiation techniques (including inverse trigonometric functions), curve sketching, optimization applications and an introduction to antiderivatives and definite integrals with applications.
(Calculus II) integral calculus, this course includes the study of Riemann Sums, antiderivative, definite and indefinite integrals, integration techniques, applications of integration, solving differential equations, convergence of sequences and series, and Taylor Series.
Upon completion of the course the students earn 4 credit hours per semester from the Central Virginia Community College.

COURSE CONTENT: At the end of the semester, the student will be able to:

Calculus I

• explain the concept of and evaluate limits
• find intervals of continuity for a function
• ‘construct’ the definition of the derivative
• explain how the secant and tangent line relate to the derivative, average and instantaneous rates of change, velocity and acceleration
• find approximations for the derivatives at a point
• use local linearity to estimate functional values
• apply appropriate techniques of differentiation (product, quotient, chain, exponential, logarithmic)
• use the definition of the derivative to derive selected derivative formulas
• differentiate trigonometric functions
• perform implicit differentiation
• find the tangent to parametric curves
• derive derivative formulas and take derivatives of inverse trigonometric functions
• use differentials to find relative and percentage error
• solve related rates applications
• determine increasing and decreasing intervals of a function
• determine concavity of a function and points of inflection
• sketch curves using appropriate techniques
• solve optimization problems
• apply Newton's method when finding roots
• setup and evaluate Riemann Sums
• interpret the definite integral
• find antiderivatives of power, ploynomial, exponential, logarithmic and trigonometric functions
• perform integration using u-substitution
• approximate the definite integral using Riemann Sums
• evaluate definite integrals using the Fundamental Theorem of Calculus
• apply the indefinite integral to position-velocity-acceleration problems

Calculus II

• interpret the definite integral
• perform integration using u-substitution, integration by parts, partial fractions, trigonometric substitution, power reduction of integrals involving trig functions and table look-up
• approximate the definite integral using Riemann Sums, Trapezoidal Rule (with error) and Simpson’s Rule with error
• apply L’Hopital’s Rule when evaluating limits
• evaluate improper integrals
• apply the definite integral (position-velocity-acceleration, growth and decay, work, force-pressure, economics, probability distributions, volumes by slicing, arc length and surface area), using rectangular and polar functions
• solve separable differential equations using tables, slope fields, numerical techniques including Euler’s Method and algebraic techniques
• solve logistic and preditor/prey population models
• determine convergence/divergence of infinite sequences
• determine convergence/divergence of geometric series
• apply integral, comparison, alternating series, absolute convergence, and ratio tests to determine series convergence/divergence
• determine radius of convergence of power series
• find Taylor and MacLaurin polynomials and Taylor and MacLaurin series with error term

COURSE OBJECTIVES: At the end of the semester, students will have an understanding of the concepts and techniques listed above.  This understanding will be enhanced, when appropriate, through directed group and individual computer exercises and group and individual projects.

HONOR CODE: Students are required to pledge all work that they turn in for a grade.  Refer to CVGS Student Handbook for complete requirements.

CLASS METHODOLOGY: Class periods will consist of a variety of activities which will include lecture (usually by me, but you may get a turn before the year is gone), group problem solving and exploration of questions and concepts using selected software.  Periodically we will have question and answer days (see course calendar for details).  Your math/tech time will also provide ample opportunity for these ventures.  It is strongly advised (shall we say required) that you prepare for each class meeting by reading the material AND by working the problems for the next class meeting.  It is solely your responsibility to prepare for class.