Single Variable Calculus

Course Objective

At the end of this course students will be able to:

• calculate limits using appropriately chosen methods, such as l'Hôpitals rule or by identifying dominant terms.
  
• calculate derivatives, find local extreme values and use these to graph functions.
  
• calculate integrals using appropriately chosen methods, such as the substitution method, integration by parts or partial fraction expansion.
  
• solve simple differential equations with or without initial data.
  
• compute Taylor polynomials and manipulate Taylor series.
  
• determine if a series converges using an appropriately chosen convergence test.
  
• write down the arguments involved in solving a calculus problem in a logically correct manner.

Course Content

This course deals with calculus of functions of one variable.

In particular we cover

• manipulating algebraically with exponential, logarithmic and (inverse) trigonometric functions
• determining limits by identifying dominant terms
• computing limits using l'Hôpital's rule
• calculating derivatives of any composition of elementary functions
• computing Taylor polynomials
• computing tangent lines to implicitly defined curves in the plane
• finding and classifying the (local) minima and maxima of functions
• graphing simple functions (e.g. rational functions, exponentials, logarithms and compositions thereof)
• calculating areas under the graphs of elementary functions
• computing antiderivatives using integration by parts
• computing antiderivatives using an appropriately chosen substitution
• integrating simple rational functions (using "partial fractions")
• determining if an improper integral converges (and compute the area)
• solving first order differential equations of separable type and of linear inhomogeneous type
• performing arithmetic with complex numbers
• determining if a series converges by comparing to a geometric series or p-series.
• determining if a series converges using an appropriately chosen convergence test
• determining the interval of convergence of a power series
• performing simple algebraic manipulations with power series
• simple analysis type epsilon proofs

Additional Information Teaching Methods

Class meetings (twice per week, 2x2=4 hours), tutorials (once per week, 2 hours)

Method of Assessment

Weekly MyMathLab exercises (10%), a homework assignment on proofs (10%), two Midterm exams (20% and 25%)

and a Final exam (35%). There is a resit that covers the material of both midterm exams, the homework assignment, and the final; the resit has a weights of 90%, with the MyMathLab exercises retaining a 10% weight.

Literature

Calculus: A Complete Course, by Adams and Essex, 9th edition, Pearson 2016. ISBN 978-0134154367

Additional Information Target Audience

Additional Information

Recommended background knowledge

Mathematics at exit level Wiskunde B or comparable