Free online courseIntroductory Calculus
Duration of the online course: 40 hours and 9 minutes
5
(1)
Master the fundamentals of calculus with this comprehensive free online course by Math for Thought, covering everything from functions to integrals. Perfect for beginners!
Course Description
Welcome to "Introductory Calculus," a comprehensive course designed to kickstart your journey into the fascinating world of calculus. With a duration of 40 hours and 9 minutes, this course promises to offer a thorough understanding of fundamental calculus concepts, perfectly suited for those embarking on their academic journey in this subject.
Highly regarded in the educational community, this course has impressively secured an average rating of 5 stars, reflecting its quality and the satisfaction of previous learners. It falls under the category of Basic Studies and is specially tailored as an introductory series in the subcategory of Calculus.
The course is thoughtfully structured to cover essential topics such as Introduction to Calculus, where you'll begin with understanding the number system and inequalities. You will explore concepts like absolute values, with specific examples and properties including intriguing triple absolute values scenarios. Building on these foundations, you will delve into a detailed discussion of functions, compositions, and inverse functions, including their trigonometric counterparts.
As you progress, the course will introduce exponential and logarithmic functions, guiding you through additional examples aimed at examining pre-calculus topics using exam-style questions. From there, you'll explore conditional statements, the principle of mathematical induction, and its application with provided examples. The journey continues into sequence convergence, monotonic sequences, and the related theorems, all bolstered with practical induction examples.
Limits and their laws form a critical part of this course. You'll learn about one-sided limits, infinite limits, and vertical asymptotes. Lessons on the Squeeze Theorem and continuity, along with the Intermediate Value Theorem, will help solidify your understanding of these core principles.
Differentiation is another cornerstone of calculus, thoroughly covered in this course. You'll master derivatives, higher-order derivatives, and various differentiation rules, including trigonometric functions and the chain rule. The course includes intricate examples and practical applications like tangent/normal lines, implicit differentiation, and logarithmic differentiation.
Beyond basic differentiation, the course extends to related rates, offers a midterm review, and introduces Taylor Polynomials and linear approximations. Partial derivatives and hyperbolic trigonometric functions are also explored, ensuring a well-rounded comprehension of these advanced topics.
Further, you will study the principles of optimization, Newton's method, sigma notation, and summation. As integral calculus comes into play, topics like the area under a curve, definite and indefinite integrals, and the Fundamental Theorem of Calculus are comprehensively taught.
Towards the end of the course, specific attention is given to L'Hopital’s rule, slant asymptotes, and curve sketching, all demonstrated with examples. Optimization problems, sigma notation, and the substitution rule round out the curriculum, ensuring you have both a theoretical and practical grasp of calculus principles.
The course concludes with a detailed final exam review, providing a robust framework to re-examine key concepts and prepare for real-world application. Join "Introductory Calculus" and take the first step towards mastering calculus with confidence, guided by a curriculum that is both thorough and highly esteemed by learners worldwide.
Conteúdo do Curso
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Video class: Calculus I: Introduction
0h10m
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Exercise: What aspect of calculus deals primarily with finding the area under curves?
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Video class: Calculus I: The Number System
0h26m
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Video class: Calculus I: Inequalities
0h25m
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Exercise: Consider the inequality x^2 - 3x - 10 < 0. What are the solutions for x?
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Video class: Calculus 1: Absolute Values
0h09m
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Video class: Calculus I: Absolute Value (Examples)
0h22m
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Exercise: Solve the absolute value equation: |3x - 6| = 9.
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Video class: Calculus I: Properties of Absolute Values and an interesting example with Triple Absolute Values!
0h13m
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Video class: Calculus I: Functions
0h19m
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Exercise: Considering the definition of a function, which of the following graphs represents a function, as per the vertical line test?
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Video class: Calculus I: Understanding and Plotting Common Functions
0h27m
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Video class: Calculus I: Compositions of Functions
0h08m
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Exercise: Given the functions \( f(x) = x + 2 \) and \( g(x) = x^2 \), what is the composition \( f(g(x)) \) and what is its domain?
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Video class: Calculus I: Inverse Functions
0h23m
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Video class: Calculus I: Inverse Trigonometric Functions
0h29m
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Exercise: What is the correct expression for the inverse function of sine, commonly known as arcsine?
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Video class: Calculus I: Exponential and Logarithmic Functions
0h31m
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Video class: Additional Examples in Pre Calculus Topics (Exam style questions)
0h37m
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Video class: Calculus I: Conditional Statements
0h22m
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Video class: Calculus I: Principle of Mathematical Induction
0h11m
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Exercise: Which of the following steps is correctly described in the principle of mathematical induction?
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Video class: Calculus I: Examples of the Principle of Mathematical Induction
0h55m
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Video class: Calculus I: Convergence of a Sequence
0h14m
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Exercise: Which of the following describes the concept of a limit in a sequence?
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Video class: Calculus I: Monotonic Sequences and the Monotone Sequence Theorem
0h08m
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Video class: Calculus I: Examples of Sequence Questions (With Induction!)
0h32m
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Exercise: Consider the sequence given by the formula: \( a_n = \frac{3n^2 + 5n}{2n^2 + n + 1} \). What is the limit of the sequence \( a_n \) as \( n \) approaches infinity?
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Video class: Calculus I: The Limit of a Function
0h21m
This free course includes:
40 hours and 9 minutes of online video course
Exercises to train your knowledge
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