MS-A0111 - Differential and Integral Calculus 1, 07.09.2020-21.10.2020

Guest access

Please note! Course description is confirmed for two academic years (1.8.2018-31.7.2020), which means that in general, e.g. Learning outcomes, assessment methods and key content stays unchanged. However, via course syllabus, it is possible to specify or change the course execution in each realization of the course, such as how the contact sessions are organized, assessment methods weighted or materials used.

LEARNING OUTCOMES

After the course the student will

- be able to analyze the convergence of sequences and series

- be familiar with the series expansions and approximations of elementary functions

- master the most important properties, calculation methods, and applications of the derivative and the integral

- be able to solve a first order differential equation in the linear and separable cases

- be able to solve a linear second order differential equation in the case of constant coefficients

Credits: 5

Schedule: 07.09.2020 - 21.10.2020

Teacher in charge (valid 01.08.2020-31.07.2022): Pekka Alestalo

Teacher in charge (applies in this implementation):

Contact information for the course (valid 01.09.2020-21.12.2112):

Harri Hakula

CEFR level (applies in this implementation):

Language of instruction and studies (valid 01.08.2020-31.07.2022):

Teaching language: English

Languages of study attainment: English

CONTENT, ASSESSMENT AND WORKLOAD

Content

  • Valid 01.08.2020-31.07.2022:

    sequences, series, power series, derivatives and integrals, basic types of differential equations

  • Applies in this implementation:

    WeekDateSubjectMaterialReference
    37Mon 7.9.
    Wed 9.9.     		Sequences, limits, functions
    Derivative     		Adams: 1 Limits and Continuity
    Adams: 2.2 Derivative
    38Mon 14.9.
    Wed 16.9.     		Optimisation, differentiation techniques
    Taylor polynomials, pointwise approximation    		Adams: 2 Differentiation
    Adams: 3 Trancendental Functions
    Adams: 4 More Applications of Differentiation
    Adams: 4.10 Taylor Polynomials
    39Mon 21.9.
    Wed 23.9.     		Definition of a definite integral as a limit
    Numerical quadratures     		Adams: 5.3 The Definite Integral
    Adams: 6.6 The Trapezoid Rule and Midpoint Rules
    40Mon 28.9.
    Wed 30.9.     		Integration techniques
    Integration by parts     		Adams: 5.6 The Method of Substitution
    Adams: 6.1 Integration by Parts
    41Mon 5.10.
    Wed 7.10.     		Ordinary differential equations
    Solution techniques, Euler's method
    Adams: 7.9 First-Order Differential Equations
    42Mon 12.10.
    Wed 14.10.     		Harmonic oscillator
    Revision     		Adams: 3.7 Second-Order Linear DEs with Constant Coefficients
    Adams: Appendix I Complex Numbers

Assessment Methods and Criteria

  • Valid 01.08.2020-31.07.2022:

    lectures, exercises, midterm exams/final exam.

Workload

  • Valid 01.08.2020-31.07.2022:

    24+24 (4+4)

DETAILS

Study Material

  • Applies in this implementation:

    Adams, Essex: Calculus, A Complete Course, 9th Ed, Pearson (and lecture notes)

Substitutes for Courses

  • Valid 01.08.2020-31.07.2022:

    Together with the course MS-A00XX Matrix algebra substitutes the courses Mat-1.1010, Mat-1.1110, Mat-1.1210, Mat-1.1310, Mat-1.1410, Mat-1.1510,

    Mat-1.1610, Mat-1.1710.

    Substitutes the courses MS-A01XX Differential and integral calculus 1.

Prerequisites

  • Valid 01.08.2020-31.07.2022:

    high school mathematics.

FURTHER INFORMATION

Description

Registration and further information

Rules of Conduct - Students´ Rights and Responsibilities (in force from 1 August 2020)

Aalto University Code of Academic Integrity and Handling Violations Thereof