After this course, the student
- is able to analyse algebraic properties of univariable functions, including critical points, limits, asymptotic behaviour and singularities
- understands the concept of Riemann integration and is able to apply this to appropriate problems
- is able to apply partial integration to find antiderivatives
- is able to analyse improper integrals
- is able to solve linear or separable non linear first order ordinary differential equations
- is able to apply 3D coordinate systems, inner and cross products, to describe and analyse properties of 3D geometrical objects and space curves
- is able to analyse and solve systems of linear equations in a finite number of variables
- understands the concept of determinant and the relation to solvability of square systems of linear equations.
- is, on an elementary level, able to use mathematical software to assist in solving mathematical problems.
In this 6 EC course you will develop your conceptual understanding of calculus of functions of one variable and linear algebra. You will be able to apply the key concepts of the course in order to solve concrete problems. You will increase your computational skills, and practice in communicating your results. You will get an elementary introduction in the use of mathematical software.|
The course will cover the concepts of limits, derivatives, integrals and ordinary differential equations, coordinates and space curves, vectors and matrices, systems of linear equations, eigenvalues and eigenvectors. The content of this course will be a foundation for any further science, engineering or even social science specializations.
Knowledge presumed as a basis:
First year students registered for the course will have to master the topics provided on the online Math Platform Grasple.
The aim of this preparatory set of units is to provide a link between the topics already taught in high school and the more advanced topics to be covered in the course Introduction to Calculus and Linear Algebra in Semester 1.
Topics to be covered and Learning Objectives:
Fundamentals (Learning Objectives):
Recall and apply basic algebra skills.
Sketch graphs of various expressions.
Find intersection points.
Solve equations and inequalities.
Unit 1: Functions (Learning Objectives)
Define a function.
Recognize different categories of functions.
Analyse the behaviour for different categories of functions.
Use the properties of these functions to solve equations and application problems.
Unit 2: Limits (Learning Objectives)
Demonstrate, describe, and recognize ways in which limits exist (or not) .
Evaluate limits given analytic, graphical, numerical function information .
Explain indeterminate form of limits.
Evaluate one sided limits.
Describe relationship between Limits and Continuity.
Unit 3: Derivatives (Learning Objectives)
State the limit definition of derivative of a function.
Calculate derivatives of functions by applying differentiation rules.
Interpret and make use of notation for higher-order derivatives.
Unit 4: Integration (Learning Objectives)
Define the First and Second Fundamental Theorem of Calculus.
Relate the Definite integral with the Area under a curve.
Solve Indefinite and Definite Integrals using appropriate Integration Rules.
Use Substitution Rule to solve integrals.
External students who are interested in this elective: please contact firstname.lastname@example.org
|James Steward, Calculus Early Transcendentals,8th edition
|Linear Algebra and its Applications, 5th Edition, David C. Lay, Pearson Education|
|Anton, Bivens, Davis, Calculus, Early Transcendentals, 10th edition
|Linear Algebra, A Modern Introduction, 4th Edition, David Poole, ISBN-13: 978-1-285-46324-7|
|Self study with assistance|
|Written examination and assignment|