微积分英文版第八版教学设计 (2)
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1 Calculus: 8th Edition Teaching Plan
Course Description
This course is designed to provide students with a solid foundation
in calculus, which can be used as a basis for further studies in
mathematics, science, and engineering. The course will cover topics such
as differentiation, integration, limits, and derivatives, and their
applications. Additional topics, such as differential equations,
multivariable calculus, and series, may also be covered.
Course Goals and Objectives
The primary goal of this course is to provide students with a deep
understanding of calculus and its applications in various fields. Upon
completion of this course, students should be able to:
• Understand the fundamental concepts of calculus, including
differentiation, integration, and limits
• Apply calculus techniques to solve problems in various
fields, such as physics, engineering, and economics
• Prove theorems and solve problems using rigorous
mathematical methods
• Work collaboratively with others to solve complex problems
• Communicate mathematical ideas and concepts in written and
oral form.
Course Outline
1. Limits and Continuity 2 – Definition of Limits
– Properties of Limits
– Limits at Infinity
– Continuity
2. Derivatives
– Definition of Derivatives
– Derivative Rules
– Derivatives of Trigonometric Functions
– Related Rates
3. Applications of Derivatives
– Motion and Optimization Problems
– Derivatives of Exponential and Logarithmic Functions
4. Integration
– Antiderivatives
– Definite Integrals
– Fundamental Theorem of Calculus
– Integration by Substitution
– Integration by Parts
5. Applications of Integration
– Area Under a Curve
– Volume and Surface Area
– Arc Length and Surface Area of Revolution 3 Teaching Strategies and Techniques
In order to help students achieve the learning objectives of this
course, a variety of teaching strategies and techniques will be used,
including:
1. Lectures: Class lectures will provide a thorough explanation
of calculus concepts and techniques, including worked examples and
problem-solving strategies.
2. Problem Sets: Regular problem sets and homework assignments
will be assigned to help students develop their problem-solving
skills and reinforce key concepts.
3. Collaborative Learning: Collaborative learning activities,
such as group problem-solving and peer instruction, will help
students work together to solve complex problems and reinforce
understanding.
4. Technology: The use of technology, such as calculators and
computer software, will be integrated into the course to help
students visualize and understand calculus concepts.
5. Assessments: Tests and quizzes will be given at regular
intervals to assess student understanding and progress.
Additionally, students may be required to complete projects or
presentations to demonstrate mastery of calculus concepts and
techniques.
Course Materials
The following materials will be used in this course: 4 • Calculus: Eighth Edition by James Stewart
• Graphing Calculator (TI-84 or equivalent)
• Computer Software (MATLAB or equivalent)
Additional materials, such as online resources and supplementary
readings, may also be provided throughout the course.
Conclusion
This teaching plan for the eighth edition of Calculus ms to equip
students with the fundamental concepts and techniques of calculus, as
well as prepare them for further studies in mathematics, science, and
engineering. Through the use of various teaching strategies and
techniques, students will develop a deep understanding of calculus and
its applications, and be able to communicate their knowledge and skills
effectively.
