ML0012 Mathematics C
KTH Royal Institute of Technology
Basic qualifications for university studies and Mathematics B from high school or equivalent.
Part of course: Exam 1
- Numbers and numerical calculations, formulas, units.
- Plan and space geometry, trigonometry of right triangles.
- Algebra: Polynomials, rational expressions, solving equations, linear inequalities.
- Functions of: Linear functions, linear equations, polynomial functions, exponential and power functions, scientific notation and logarithms. Solving equations
Part of course: Exam 2
- Changes in speeds and derivatives, chain rule (introduction). Curves and derivatives, extreme values, maximum and minimum value.
- Arithmetical and geometrical sequences and sums
OVERALL GOALS
The student will be given a basic understanding of and skills in mathematics, needed to be able to understand the mathematics courses, as part of the college and engineering programs.
Part of course: Exam 1
The student will after the course to:
- deal with numerical calculations with real numbers, written in different ways
- manage formulas
- calculate the correct devices enter perimeter and area for a few simple areas and areas and volumes of some simple cells
- using key rates and know the concepts of classical geometry
- apply trigonometry in right triangles
- simplify and transform algebraic polynomial expressions
- solve equations of the first and second degree, linear inequalities, root equations and also polynomial equations of higher degree by factoring or by substitution
- simplify and use rational expressions and solve equations containing rational expressions
- interpret and use the powers and logarithms with real exponents, and master the relevant laws such as counting the solution of equations
- explain the characteristics of linear and some non-linear functions
- work with linear equations in different forms, solve systems of equations using algebraic methods, and interpret the solution from the graphical view
- determine the maximum and minimum points by using the symmetry of the quadratic function
- set up, interpret, and illustrate linear functions, power functions and exponential functions as models of real events in different areas
- use their skills in problem solving and in their study subjects
Part of course: Exam 2
The student will after the course to:
- explain, illustrate, use and interpret the concept of changing coefficients and derivatives of a function and use these to describe the characteristics of a function and its graph
- derive and use the rules of differentiation for some basic power functions, exponential functions and use the chain rule
- describe why and how the number e is introduced
- to draw conclusions about a function's derivative and estimate the value of the derivative when the function is given by its graph
- use the relationship between a function's graph and its derivatives in different application contexts
- use mathematical models of various kinds, including those based on arithmetic and geometrical progressions
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