Course syllabus for Calculus

The course syllabus contains changes
See changes

Course syllabus adopted 2021-03-15 by Head of Programme (or corresponding).

Observe
Note – can not be included in a Chalmers' degree

Overview

  • Swedish nameMatematik
  • CodeMVE641
  • Credits28.5 Pre-education credits
  • OwnerZBASD
  • Education cyclePre-university
  • DepartmentMATHEMATICAL SCIENCES
  • GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail

Course round 1

  • Teaching language Swedish
  • Application code 96116
  • Open for exchange studentsNo

Credit distribution

0121 Examination, part A 7.5 fup
Grading: TH		7.5 fup
  • 26 Okt 2021 am L
  • 03 Jan 2022 pm L
  • 16 Aug 2022 pm L
0221 Examination, part B 7.5 fup
Grading: TH		 7.5 fup
  • 14 Jan 2022 pm L
  • 15 Feb 2022 pm L
  • 24 Aug 2022 pm L
0321 Examination, part C 7.5 fup
Grading: TH		 7.5 fup
  • 17 Mar 2022 pm L
  • 13 Apr 2022 pm L
  • 18 Aug 2022 pm L
0421 Examination, part D 4.5 fup
Grading: TH		 4.5 fup
  • 06 Maj 2022 pm L
  • 30 Maj 2022 pm L
  • 19 Aug 2022 pm L
0521 Laboratory 1.5 fup
Grading: UG		 1.5 fup

In programmes

Examiner

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Eligibility

General entry requirements for bachelor's level studies

Specific entry requirements

Mathematics 2a or 2b or 2c or equivalent and English 6

Course specific prerequisites

Examination certificate from upper secondary school including or complemented by the courses 2a or 2b or 2c in mathematics.

Aim

The aim of the course is to give basic knowledge in mathematical analysis. The course will also supply a good base for further studies.

Learning outcomes (after completion of the course the student should be able to)

  • understand how mathematics is build on definitions and theorems.
  • simplify algebraic expressions.
  • solve systems of linear equations system.
  • use the laws of exponens.
  • fundamental geometry.
  • fundamental trigometric.
  • solve trigonometric equations.
  • solve inequalitys.
  • define absolute value.
  • define the concepts of limit and continuity and calculate limits.
  • define the concepts of derivative and differentiation and use the definition of derivative.
  • calculate the derivatives of elementary functions.
  • use the fundamental rules of differentiation.
  • outline the elementary functions and account for their properties.
  • define the concepts of increasing (decreasing) function and local maximum (minimum) value.
  • construct graphs of functions and calculate the absolute maximum (minimum) value of a function.
  • define the concept of inverse function, calculate inverse functions and their derivates.
  • calculate with complex numbers.
  • solve algebraic equations.
  • understand the concept of sequences and be able to handle arithmetic and geometric sequences.
  • understand the concept of recursion and be able to handle recursively defined sequences.
  • understand and use sigma notation.
  • calculate arithmetic and geometric sums.
  • use the technique of mathematical induction.
  • define the concepts of antiderivative, definite integral and improper integral.
  • use the fundamental rules of integration.
  • use the most common methods for solving differential equations.
  • formulate, and in certain cases prove, fundamental theorems in analysis as, e g the connection between continuity and differentiation, the connection between area and antiderivatives and the mean-value theorem.
  • interpret limits, derivatives and integrals geometrically.
  • apply his/her knowledge of derivatives and integrals to simpler applied problems.
  • understand and be able to handle basic concepts in set theory, propositional logic and integer arithmetic.
  • understand, and be able to solve, simple combinatorial problems.
  • basics in programming with applications in mathematics.

Content

  • Module A (7.5 cr): Real numbers. Algebra: operations with algebraic expressions, expanding and factoring of polynomials, division of polynomials, roots, equations, systems of linear equations, inequalities. Trigonometry: angles, arc length and sector area, cosine, sine, tangent, cotangent, Functions of one variable: polynomials, rational functions.
  • Module B (7.5 cr): Absolute values. Exponential and logarithmic functions. trigonometric formulas, trigonometric equations. trigonometric functions. Functions of one variable: limits, continuity.
  • Module C (7.5 cr): Derivatives, applications, maxima and minima. Differentiation rules: sums, constant multiples, the chain rule, the product rule, the quotient rule, composite functions. Derivatives of higher orders with applications. Graphs of functions. Sequences and recursion, sums and sigma notation, indefinite and definite integrals, integration by substitution, integration by parts, integrals of rational functions and some transcendental functions, areas of plane regions and other applications of integrals. Ordinary differential equations with applications.
  • Module D (4.5 cr): Arithmetic and geometric sequences and sums. Induction. Set theory, logic and integer arithmetic. Combinatorics./li>
  • Programming (1.5 cr). Variables, assignment, combine commands, handle numbers and elementary functions, script files, vectors, plots in 2D, logical expressions and relational operators, character field, input and output, conditional statements (if), loops (for and while), error handling, short about data types, functions and function files, recursive functions, short about algorithms and numerical methods with examples, short about flowcharts and pseudocode.

Organisation

Teaching takes place online through lectures and exercises.

Literature

Håkan Blomqvist: Matematik för tekniskt basår, del 1¿3, Matematiklitteratur. Complementary materials in combinatorics and discrete mathematics.

Examination including compulsory elements

Written examinations, both digitally and on Campus, are carried out for the modules A, B, C and D. Grading TH. The examination of the programming module is web-based. Grading UG. Completed course corresponds to depth and content at least the upper secondary school's course Mathematics 4.

The course examiner may assess individual students in other ways than what is stated above if there are special reasons for doing so, for example if a student has a decision from Chalmers about disability study support.

The course syllabus contains changes

  • Changes to examination:
    • 2022-02-01: Examination time Examination time changed from Morning to Afternoon by Monika Tykesson
      [2022-03-17 7,5 hec, 0321]
    • 2022-02-01: Examination datetime Examination datetime changed from 2022-05-30 Morning to 2022-05-30 Afternoon by Tommy Gustafsson
      [2022-05-30 4,5 hec, 0421]
    • 2022-02-01: Examination datetime Examination datetime changed from 2022-05-17 Morning to 2022-05-06 Afternoon by Tommy Gustafsson
      [2022-05-17 4,5 hec, 0421]
    • 2022-02-01: Examination datetime Examination datetime changed from 2022-04-12 Morning to 2022-04-13 Afternoon by Tommy Gustafsson
      [2022-04-12 7,5 hec, 0321]
    • 2021-10-20: Examination time Examination time changed from Morning to Afternoon by Elisabeth Eriksson
      [2022-02-15 7,5 hec, 0221]
    • 2021-10-20: Examination time Examination time changed from Morning to Afternoon by Elisabeth Eriksson
      [2022-01-14 7,5 hec, 0221]