Far too many students begin a Differential Equations course lacking basic skills from first-year calculus.  These skills should be reviewed and brushed up (and in some cases, learned for the first time).  The references given here are for first-semester calculus and are mostly concerned with differentiation and some of its applications and interpretations. 

Integration technique is also required for this course.  This includes:

• basic u-substitution

• integration by parts

• partial fractions and

• trigonometric subsitutions. 

Review materials for integration technique and differentiation are widespread.  Khan Academy is one excellent source and is easily accessed.

Documents related to first-semester calculus are included below:

For a review of first-semester calculus:

 

The page http://vhcc2.vhcc.edu/cal1fall/ is the homepage for the instructor's Calculus I course.  The Open QA's for that course would provide a good review of the basic topics covered in most first-semester classes, and should at least give you a good start on some of the topics that might not have been covered in your first-semester course. 

The coverage of topics is roughly as follows:

The open qa's for Assignments 11-12 cover the rules of differentiation.

The open qa's for Assignments 13-15 introduce applications of differentiation, tangent lines and the differential.

The open qa for Assignment 16 addresses implicit differentiation. 

The open qa's for Assignments 1-10 introduce you in a unified way to the concepts of differentiation and integration, beginning with the concept of rate of change. 

The open qa for Assignment 10 is fairly challenging and introduces the central ideas of integration in the context of finding present and future values of an investment. 

Most multivariable calculus students will benefit greatly from this refresher on standard first-semester calculus topics.  All these ideas extend into three dimensions and therefore appear in Multivariable Calculus.

A listing of the Calculus I qa's, in the order mentioned above, follows:

• qa11 on the rules of differentiation for the basic functions
• qa12 on the product, quotient and chain rules
• qa13 on applications of the chain rule
• qa14 on tangent line approximations
• qa15 on the differential and the tangent line
• qa16 on implicit differentiation

 

• qa01 on the idea of rate of change
• qa02 more about the idea of rate of change
• qa03 graphical representation of rate of change
• qa05 average rate of change, changing rate of change
• qa06 finding change in quantity given rate of change information
• qa07 rate of change functions
• qa08 approximate depth graph constructed from rate function
• qa09 predictor-corrector

 

• qa10 income streams