For each of the four courses in the Calculus sequence, the following topics and corresponding sections of the course textbook (Calculus, Early Transcendentals, by Stewart) are likely to be covered by the instructor. The exact topics covered will be chosen by the instructor, and will vary somewhat from section to section.
Calculus I
Functions and Models (Chapter 1)
Limits and Derivatives (Chapter 2)
Differentiation Rules (Chapter 3)
Applications of Differentiation (Chapter 4)
Integrals (Chapter 5)
Applications of Integration (Chapter 6)
Areas between Curves (6.1)
Optional topics:
More applications of integration from Chapter 6
Typical Syllabus
Calculus II
Review of Integration and Applications
Review of trigonometry (Appendix D) and complex numbers (Appendix H)
Techniques of Integration (Chapter 7)
(may not necessarily include approximate methods, 7.7)
Further Applications of Integration (Chapter 8)
Arc Length (8.1)
Parametric Equations and Polar Coordinates (Chapter 10)
Curves defined by parametric equations (10.1)
Calculus with parametric curves (10.2)
Polar coordinates (10.3)
Areas and lengths in polar coordinates (10.4)
Infinite Sequences and Series (Chapter 11)
Optional topics:
More applications from Chapter 8
Differential Equations (Chapter 9)
Conic sections from Chapter 10
Typical Syllabus
Calculus III
Vectors and the Geometry of Space (Chapter 12)
(including Conic sections, 10.5)
Vector Functions (Chapter 13)
(arc length and curvature, 13.2, is an optional topic)
Partial Derivatives (Chapter 14)
Note: problems will not be assigned from these chapters that require use of the techniques of integration taught in Calculus II.
Typical Syllabus
Calculus IV
Multiple Integrals (Chapter 15)
Vector Calculus (Chapter 16)
Another topic, e.g. complex or Fourier analysis. Suitable notes for complex analysis are here: Complex Functions 1, Complex Functions 2 and Complex Functions 3.
Typical Syllabus
