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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.

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• 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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