Calculus IA: Limits and differentiation

Mastering precalculus such as in high school mathematics curriculum is necessary. Students are expected already be able to

• Solve polynomial, rational, trigonometric, exponential equations among others
• Perform algebraic and trigonometric manipulations and rewritings to mathematical expressions
• Be familiar with basic functions and their properties
• Draw graphs of functions, be able to explain where in the graph a function is increasing or decreasing, where does it attain its minimum or maximum values, etc.

• Understand basic concepts of real-valued functions, especially what is meant by limit of a function and continuity.
• Be familiar with consequences of continuity, especially Bolzano's Theorem, and apply them for example in finding solutions to equations.
• Be able to find limits of sequences of real numbers and real valued functions with various techniques involving algebraic manipulations or with the squeeze theorem.
• Understand concept of the derivative from number of perspectives, e.g. as instantaneous rate of change, limit of so called difference quotient, slope of the tangent line to the graph of a continuous function at a point, and through differentiability.
• Find derivatives of basic functions, derive differentiation rules and apply them.
• Be familiar with Mean Value Theorem for differentiation, be able to justify why it holds, as well as use it in applications.
• Use derivative as a tool for studying behavior of functions and in other applications.

Equivalences to other courses

This is part in a series of online Calculus courses. The collection of the three courses

• MAT11006: Calculus IA: Limits and Differentiation •
• MAT11007: Calculus IB: Integration
• MAT11008: Advanced Calculus

correspond to the collection of the three Finnish analysis courses

• MAT11003 Raja-arvot
• MAT11004 Differentiaalilaskenta
• MAT11005 Integraalilaskenta

However, no single course in either collection can substitute a course from the other.

Completion methods

This is an online course. All course material and activities can be found on the online course area. There is a final proctored paper and pencil exam at the end of the course.

Evaluation methods and criteria

The lecture course will be evaluated based on course work and/or course exam.

Activities and methods supporting learning 

Homework.

Study module

Fits many study modules, for instance MAT110 Mathematics, Basic Studies

Teaching languages

English, Finnish, Swedish