Mathematics from high school to university
Instructed by Hania Uscka-Wehlou 50 hours on-demand video & 379 downloadable resources
What you’ll learn
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How to solve problems concerning exponentials or logarithms (illustrated with 239 solved problems) and why these methods work.
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Applications of exponential and logarithmic functions in finance, engineering, and natural sciences (some of them in my videos, some as reading material).
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Binomial Theorem with two proofs (a combinatorial one and one by induction), Pascal’s Triangle, and how to apply them.
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Definitions of Euler’s number e, how to approximate it, and how to prove that this number is irrational.
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Definitions and computational rules for powers with various types of exponents (natural, integer, rational, real).
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Definition of logarithms in relation to exponents, with computational rules (these will be related to the rules for powers).
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Exponential functions, their properties and graphs.
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Logarithmic functions, their properties and graphs.
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Power functions, their properties and graphs; interactions between power functions and exponential functions.
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Graph transformations for exponential and logarithmic functions, and for some power functions.
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Solving exponential equations and inequalities.
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Solving logarithmic equations and inequalities.
Who this course is for:
- Students who plan to study Algebra, Calculus or Real Analysis
- High school students curious about university mathematics; the course is intended for purchase by adults for these students
- Everybody who wants to brush up their high school maths and gain a deeper understanding of the subject
- College and university students studying advanced courses, who want to understand all the details (concerning exponentials and logarithms) they might have missed in their earlier education
- Students wanting to learn exponentials and logarithms, for example for their College Algebra class.
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