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Calculus 2 is a math course also known as second-semester calculus or integral calculus that is a more advanced version of Calculus 1 and is taken after the completion of Calculus 1. It is an important course for students pursuing degrees in areas such as math, physics, engineering, and economics. You’ll learn the following topics in calculus 2:
Sequences are ordered lists of numbers or terms, while series are the sums of terms in a sequence. In sequence & series, students will learn how to identify arithmetic and geometric sequences and series, and to find their sums. They will also learn how to use formulas for finding the nth term of a sequence and the sum of a finite arithmetic or geometric series.
With these skills, students should be able to understand and analyze patterns in numerical data and be able to make predictions about future values based on patterns in the data. They will also be able to identify and use formulas for sequences and series to solve problems in various real-life situations, such as financial investments, population growth, and mathematical modeling.
In differential equations, students will learn about various methods for solving different types of differential equations, including separable equations, linear equations, and homogeneous equations. They will also learn how to apply these methods to solve real-world problems, such as modeling population growth, radioactive decay, and circuit analysis.
After all this knowledge, they will be able to apply their knowledge of differential equations to solve problems in a variety of fields, including physics, engineering, and economics. They will also develop an understanding of the importance of differential equations in modeling real-world phenomena, such as motion, heat transfer, fluid dynamics, and electromagnetism.
In integration techniques, students will learn about more advanced integration techniques that they learned in Calculus 1. They will also learn how to integrate using techniques such as integration by parts, trigonometric substitution, partial fractions, and numerical integration and how to apply these techniques to solve real-world problems, such as finding the area between curves and the volume of solids of revolution.
After gaining this knowledge, they will be able to use these integration techniques to evaluate a wide range of integrals that cannot be solved using basic methods. They will also be able to apply these techniques to solve various real-world problems involving integration, such as finding the work done by a variable force and determining the average value of a function over an interval.
In the application of integration, students will learn about the methods of integration, including integration by substitution, integration by parts, and trigonometric substitution, and how to apply these integration techniques to solve problems involving motion, work, and fluid pressure. They will also learn how to find the center of mass and moments of inertia of objects using integration.
After gaining this knowledge, they will be able to use integration to solve a wide range of real-world problems, such as finding the volume of an irregularly shaped container, calculating the force required to move an object through a fluid, and determining the work required to lift an object against gravity.
In parametric equations, students will learn about 2-dimensional figures, such as triangles, quadrilaterals, and polygons, and explore their properties and relationships and 3-dimensional figures, such as prisms, pyramids, cones, and spheres, and how to calculate their surface area and volume. They will also learn how to these figures to identify congruent and similar figures.
In the end, they will be able to identify and classify geometric shapes, including triangles, quadrilaterals, and circles, and how to calculate the perimeter, area, and volume of these shapes. They will also be able to use geometric constructions to create various shapes, such as perpendicular and parallel lines, and to bisect line segments and angles.
In polar coordinates, students will learn how to represent curves using parametric equations, differentiate and integrate parametric equations, about polar coordinates, how they can be used to describe the location of points in the plane. They will also learn about the relationship between polar coordinates and rectangular coordinates, how to convert between the two systems, the concepts of area and arc length in polar coordinates, and how to apply integration techniques to calculate these quantities for various curves.
With these skills, students will be able to solve problems related to parametric equations and polar coordinates, including finding tangents and areas of curves, determining symmetry of graphs, and identifying conic sections.
Learning calculus 2 has many benefits, such as:
Overall, learning calculus 2 provides students with the tools and skills necessary to succeed in higher education and in other related careers.
Wiingy online Calculus 2 tutor can provide you with many benefits, such as:
Accumulations of change introduction
Approximation with Riemann sums
Summation notation review
Riemann sums in summation notation
Defining integrals with Riemann sums
Fundamental theorem of calculus and accumulation functions
Interpreting the behavior of accumulation functions
Properties of definite integrals
Fundamental theorem of calculus and definite integrals
Reverse power rule
Indefinite integrals of common functions
Definite integrals of common functions
Integrating with u-substitution
Integrating using long division and completing the square
Integrating using trigonometric identities
Trigonometric substitution
Integration by parts
Integrating using linear partial fractions
Improper integrals
Differential equations introduction
Verifying solutions for differential equations
Sketching slope fields
Reasoning using slope fields
Approximation with Euler’s method
Separation of variables
Particular solutions to differential equations
Exponential models
Logistic models
Average value of a function
Straight-line motion
Non-motion applications of integrals
Parametric equations intro
Second derivatives of parametric equations
Arc length
Vector-valued functions
Planar motion
Polar functions
Arc length
Calculator-active practice
Convergent and divergent infinite series
Infinite geometric series
nth-term test
Integral test
Harmonic series and p-series
Comparison tests
Alternating series test
Ratio test
Absolute and conditional convergence
Alternating series error bound
Taylor and Maclaurin polynomials intro
Lagrange error bound
Power series intro
Function as a geometric series
Maclaurin series of eˣ, sin(x), and cos(x)
Representing functions as power series
Telescoping series
MATH 2414: Calculus II
Math 181: Calculus II
MTH 211: Calculus II
Math 1132Q : Calculus II
MA 16020: Applied Calculus II
MATH 0230: Analytic Geometry and Calculus 2
MATH-UA.0122: Calculus II
MTH 142LR: College Calculus 2
MATH 111: Techniques of Calculus II
MATH 22200 : Calculus for Technology II
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" I have always been a bright student but the concept of ‘polar coordinates’ in calculus 2 was the thing that was holding me back. Once I joined the tutoring sessions of Wiingy, my tutor explained that concept so easily in form of a story that it took less than an hour to completely grasp it. My tutor also cleared all my queries related to the concept and his hard work is the reason behind my amazing scores in exams. "
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US
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Robert
UK
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What is the purpose of calculus 2?
The purpose of Calculus 2 is to expand on what was learned in Calculus 1 and teach students more advanced techniques for solving problems that involve calculus. In this course, students learn about topics like integration techniques, sequences and series, polar coordinates, differential equations, and much more. The goal is to give students a deeper understanding of calculus and how to use it to solve real-world problems.
How fast can I learn Calculus 2?
You can expect to spend anywhere between three to six months to learn Calculus 2 You need to spend at least 2 weeks learning the calculus 1 concepts because only after learning calculus 1, you will be qualified to learn calculus 2. Later, you need to spend 1 month on integrals and application of integrals as they are complex topic and require extra attention. After that, the remaining topics of calculus 2, such as sequence & series, differential equations, parametri equations require another 3 to 4 months to complete. However, if you have a good hold over calculus 1 concepts, then you can learn Calculus 2 in two to four months, as well.
What should you know for Calculus 2?
A good foundation of Calculus 1 is essential as you start to learn Calculus 2. List of Calc 1 topics that you need to know prior to learning Calculus 2 are as follows Functions and their properties, including domain and range, composition, and inverse functions. Limits and continuity, including how to evaluate limits and identify discontinuities. Derivatives and their applications, including related rates, optimization, and curve sketching. Integration and its applications, including finding areas and volumes of revolution using integration.
How to master Calculus 2?
To master Calculus 2, focus on understanding the basic concepts of calculus 1, such as limits, derivatives, and integrals. Among all the calculus 1 concepts, derivatives and integrals are the topics that require extra attention, so you need to practice a lot of problems on these topics to understand them better. Although, if you have a good hold over all the calculus 1 concepts, then calculus 2 might be easy for you. You should also refer to resources available online, like textbooks, YouTube videos, and online tutorials. As per the students studying calculus 2, the best textbooks to refer to for calculus 2 are: How to Ace the Rest of Calculus by Colin Adams Calculus II for Dummies by Mark Zegarelli Calculus by Stewart for Cal 1-3 Apart from textbooks, referring to YouTube channels has also always been a good option, so the best YouTube videos to refer to for calculus 2 are: Calculus 2 lectures by Professor Leonard Calculus 2 lectures by Khan academy Calculus 2 by PatrickJMT Similarly for online tutorials, you can get plenty of tutorials available online which you can try and make your decision. A great way to master Calculus 2 is to take private lessons from an expert tutor. Explore Wiingy Calculus 2 tutoring online today. Book a free trial lesson with a top Calculus 2 tutor today!
What do most tutors charge for calculus 2?
Online Calculus 2 tutors typically charge between $35 to $70 per hour. However, the price of tutors will vary depending on their qualifications and level of experience. So, experienced private tutors can charge around $65 to $80 per hour. Part-time tutors typically charge between $20 and $35 per hour.
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