This course starts with four major ideas: limits, derivatives, indefinite integrals and definite integrals. Then it delves into their applications. From there it goes on to cover series and sequences, parametric and polar equations, vectors in a plane and advanced integration techniques. You will learn how to work with functions represented in a variety of ways: graphical, numerical, analytical and verbal. You will come to understand the “derivative” in terms of a limit of a rate of change and the “definite integral” as a limit of sums and the net accumulation of change.
The philosophy and approach of the course will be: to develop skills that can be applied to solving problems – skills that will become second nature because you will understand the why behind the major ideas. And you will be able to communicate the mathematics and the why both orally and in well-written sentences.
You’ll be interacting with your classmates and me, as well as posting solutions to problems, on a continual basis through an online discussion board. Each assignment will build on previous assignments, so success will depend on your daily response to the challenge.
You will start using your graphing calculator soon after the start of the class. Throughout the course of the year, you will become comfortable using it as a tool to help solve problems, experiment, interpret results, and verify conclusions. However, it will not become a replacement for your pen and pencil.
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Objectives: The successful student will:
- exhibit a proficiency in the topics covered in this course
- engage in logical and critical thinking
- demonstrate the solution to problems by translating the stated description of the problem into mathematical terms, interpreting information, sketching relevant diagrams, analyzing given data, formulating mathematical statements, then checking and verifying results
- be prepared for the Advanced Placement Exam
- be prepared for college calculus and for courses which use calculus.
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Proficiencies: Students Should Be Able To:
- work with functions represented in a variety of ways: graphical, numerical, analytical, or verbal. They should understand the connections among these representations
- understand the meaning of the derivative in terms of a rate of change and local linear approximation and should be able to use derivatives to solve a variety of problems
- understand the meaning of the definite integral both as a limit of Riemann sums and as the net accumulation of change and should be able to use integrals to solve a variety of problems
- understand the relationship between the derivative and the definite integral as expressed in both parts of the Fundamental Theorem of Calculus
- communicate mathematics both orally and in well-written sentences and should be able to explain solutions to problems.
- model a written description of a physical situation with a function, a differential equation, or an integral
- use technology to help solve problems, experiment, interpret results, and verify conclusions
- determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measurement
- develop an appreciation of calculus as a coherent body of knowledge and as a human accomplishment.
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