Mathematics 4 for Foundation Year, 8 fup

Aim

The course aim is to give a foundation in mathematics and a preparation for further university studies in mathematics.After completion of the course, the student should be able to,

• handle simple algebraic expressions with real and complex numbers.
• set up and solve equations and inequalities.
• handle and use the principle for derivatives with applications.
• apply the definition of the derivative to illustrate general differentiation rules and handle differentiation rules.
• study the elementary functions with derivates and limits to draw conclusions regarding the properties of the functions.
• use standard techniques to calculate antiderivatives and definite integrals with applications.
• use the unit circle to defined trigonometric identities, solve trigonometric equations and graph trigonometric functions.
• use programming as a tool for problem solving.

Content

Complex numbers in different forms, conjugate and absolute value of complex numbers, Euler´s formula, proof of de Moivre´s theorem with applications. Polynomials, polynomial equations with complex roots, power equations of degree one, two , three or more, factoring polynomials (Fundamental theorem of algebra), trigonometric expressions and identities, trigonometric functions, trigonometric equations, radians, logarithmic functions, absolute value function, derivatives of elementary functions (of powers, exponential and logarithmic functions, trigonometric functions), differentiation rules (sum rule, product rule, quotient rule, chain rule), study of functions, draw a curve, asymptotes. Primitive functions and integrals with applications, integration by parts, differential equations and solutions.