The aim of this course is to focus on the pre-university Calculus (functions, equations, differentiation, and integration), vector calculus (preparation for mechanics and dynamics courses) and differential equations. In addition to these, it also covers topics such as Calculus, functions of several variables, linear algebra and probability, and Statistics.

**Assessment**

This course does not involve any written exams. Students need to answer 5 assignment questions to complete the course, the answers will be in the form of written work in pdf or word. Students can write the answers in their own time. Each answer needs to be 200 words (1 Page). Once the answers are submitted, the tutor will check and assess the work.

**Certification**

Edukite courses are free to study. To successfully complete a course you must submit all the assignment of the course as part of the assessment. Upon successful completion of a course, you can choose to make your achievement formal by obtaining your Certificate at a cost of £49.

Having an Official Edukite Certification is a great way to celebrate and share your success. You can:

- Add the certificate to your CV or resume and brighten up your career
- Show it to prove your success

Course Credit: TU Delft

### Course Curriculum

Module: 1 | |||

Preview complex numbers | 00:05:00 | ||

Complex Numbers | 00:08:00 | ||

Partial Derivatives | 00:04:00 | ||

Chain rule | 00:06:00 | ||

Directional Derivative | 00:05:00 | ||

Domains and maxima | 00:04:00 | ||

Preview integration5050 | 00:03:00 | ||

Double integral | 00:08:00 | ||

Module: 2 | |||

Polar coordinates | 00:07:00 | ||

Curves and regions in polar coordinates | 00:04:00 | ||

Triple integral | 00:07:00 | ||

Cylindrical coordinates | 00:04:00 | ||

Spherical coordinates | 00:08:00 | ||

System of Linear Equations | 00:06:00 | ||

Vectors and Linear Combinations | 00:06:00 | ||

Solution Sets of Linear Equations | 00:06:00 | ||

Module: 3 | |||

Matrix Transformations | 00:07:00 | ||

Matrix Multiplication | 00:05:00 | ||

Inverse Matrices | 00:05:00 | ||

Linear Subspaces | 00:06:00 | ||

Dimensions | 00:06:00 | ||

Determinants | 00:04:00 | ||

Cramer’s rule | 00:07:00 | ||

Module: 4 | |||

Inner Product and Orthogonality | 00:07:00 | ||

Orthogonal Projections | 00:05:00 | ||

The Gram-Schmidt Process | 00:05:00 | ||

Least-squares Problems | 00:07:00 | ||

Eigenvectors and Eigenvalues | 00:07:00 | ||

Diagonalisable Matrices | 00:06:00 | ||

Complex Eigenvalues | 00:04:00 | ||

Module: 5 | |||

Systems of Linear Differential Equations | 00:07:00 | ||

Symmetric Matrices | 00:07:00 | ||

Quadratic Forms | 00:04:00 | ||

True/False Questions Part I | 00:07:00 | ||

True/False Questions Part II | 00:07:00 | ||

Preview differentiation | 00:05:00 | ||

Direction Field | 00:04:00 | ||

Module: 6 | |||

Searching for solutions | 00:08:00 | ||

The integrating factor | 00:09:00 | ||

Separable differential equations | 00:07:00 | ||

First Order Linear Differential Equations | 00:07:00 | ||

Pendulum | 00:05:00 | ||

Solving nonhomogeneous second-order differential equations | 00:07:00 | ||

Solving nonhomogeneous second-order differential equations | 00:07:00 | ||

Bayes’ rule | 00:07:00 | ||

Module: 7 | |||

Independence of events | 00:05:00 | ||

Binomial coefficients | 00:07:00 | ||

Continuous random variables | 00:08:00 | ||

Expectation of a random variable | 00:05:00 | ||

Jensen’s inequality | 00:07:00 | ||

Independence of random variables | 00:07:00 | ||

Poisson Process | 00:09:00 | ||

Module: 8 | |||

Summation notation | 00:03:00 | ||

Preview Taylor polynomials | 00:05:00 | ||

Taylor polynomials | 00:10:00 | ||

Preview Fourier Series | 00:03:00 | ||

Union and Intersection | 00:06:00 | ||

Complement and Difference | 00:03:00 | ||

Averages and Chebyshev’s inequality | 00:05:00 | ||

Module: 9 | |||

Graphical representation of data | 00:07:00 | ||

Numerical representation of data | 00:08:00 | ||

Unbiased Estimators | 00:07:00 | ||

Maximum Likelihood Principle | 00:06:00 | ||

Confidence intervals | 00:07:00 | ||

Testing hypotheses | 00:08:00 | ||

The t-test | 00:05:00 | ||

Module: 10 | |||

What is a vector? | 00:08:00 | ||

Length of a vector | 00:05:00 | ||

Dot-product | 00:08:00 | ||

Orthogonal projections – part 1 | 00:02:00 | ||

Orthogonal projections – part 2 | 00:05:00 | ||

Cross product | 00:07:00 | ||

Cross product applications | 00:05:00 | ||

Lines and planes | 00:07:00 | ||

Assessment | |||

Submit Your Assignment | 00:00:00 | ||

Certification | 00:00:00 |

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